It's gone 9.50 as I sit gnawing on Spain's version of a hotdog and waiting for Bruce Springsteen and his old gang, back together for the first time in five years with a new album, and here in Madrid's Palacio de Deportes to kick off the European leg of their world tour. They're nearly an hour late, but then, famously, nobody in this town goes to bed until it's time to get up again and this vast, roiling football crowd of an audience - roaring at every flicker on stage like dogs barking at aeroplanes - seems happy just to be in the building.

There's a lot of love here and it's not just coming from middle-aged insurance salesmen. No, I see marauding twenty- and thirtysomethings draped in American livery and even a group of squealing popteen blondes. The oldest person I notice is Martin Scorsese, hunched between burly companions two seats in front of me. The weight of anticipation is immense.

I wish, though, I'd seen Springsteen back in 1975, when I was young and open-mouthed at Bruce's thrilling scenarios of burnt-out Chevrolets and highways jammed with broken heroes, of escape and romance, suddenly alive to the inkling of perhaps getting a girl to walk with me out on the wire, to strap her hands across my engines. True, the Leeds branch of National Tyre Service (where I worked in the office) was a long way from New Jersey, but who's to say I wasn't born to run too?

I stayed with Springsteen for a couple of LPs after that. I even liked the gloomy Nebraska. But I couldn't quite bring myself to sing along to his bounceback anthem 'Born in the USA' (albeit widely misread as a new battle hymn of the republic) - and what was Bruce thinking when he pulled the young Courteney Cox on stage for a wooden-legged bop in that 'Dancing in the Dark' video in 1984? For some of us, in becoming big he became smaller.

But that was then. In recent years a more earnest Springsteen has drawn himself back, confining himself to rootsy, acoustic adventures. The sombre Devils and Dust (2005) had some nice raspy wooden things for one's iPod, then last year he recorded with the Seeger Sessions Band and went on the road mob-handed, whacking out old folk songs, country hoedowns and civil rights anthems on banjos, squeezeboxes, fiddles and penny whistles. Was Springsteen, in embracing this purer, less cynical age of protest (mixing the likes of 'We Shall Overcome' with sepia-tinted reworkings of his own songs), looking for something that carried a more authentic political charge?

Those who perhaps also sensed a dignified retreat from the rock'n'roll fray will have been surprised by his dazzling new album, Magic, a return to the echo and thunder of massed guitars, horns and swirling keyboards that became in the Seventies and Eighties the signature sound of Springsteen's heartlands America. But while the songs here ring still with the familiar themes of labour, love, struggle and flight, there is a maturer craft that illuminates his purpose as a global citizen without everyone having to punch the air.

It's these songs, rather than the classics, that I haven't been able to get out of my head since I got here. And I'm not the only one. When Springsteen and the band explode onstage with the album's opener, 'Radio Nowhere' - a killer song with a moreish jangling riff - it seem the entire audience knows the words ('Is there anybody alive out there... ').

'Hello Madrid,' Bruce bellows. 'Is there anybody home out there?' He doesn't wait for the obvious answer but launches into 'No Surrender' - adopted as a battle song by the abortive John Kerry campaign in 2004 - then 'Lonesome Day' from The Rising. Springsteen is as frenetic as ever. Nobody expects him to slide the length of the stage on his knees any more, but he's still a man with his clothes on fire, dashing from pillar to post, trading licks with 'Miami' Steve Van Zandt (better known, bizarrely under these circumstances, as Sil from the Sopranos) or mooching with 'Big' Clarence Clemons on tenor sax, or running down to the moshpit and thrashing his guitar inches from the outstretched hands of the heaving masses. Even the more contemplative interlude of 'Magic' ('Trust none of what you hear, and less of what you see') crackles with a coiled energy as he hisses at the audience to keep their racket down - a moment that recalls an incident in recent times during one of the acoustic shows when he had someone ejected for using a mobile phone. He's not called the Boss for nothing. Everyone is on their feet.

Springsteen has the look of someone who ages well, rewarded perhaps for keeping faith with his background and calling. He still dresses like a 1950s steel worker; he still has the hair of someone who likes to wrestle dogs; he has resisted the lure of Hollywood teeth. The tuft of Waitsian beard under his lip reminds us of his recent dalliances with the classes of 'un-rock', but this is a blue-collar night - and no one makes entertainment look more like manual labour.

The eight-piece E Streeters are stunning - Nils Lofgren's howling guitars, Roy Bittan's joyous piano fills, the crisply engineered swing and batter of Max Weinberg on drums. And Springsteen loves these guys, spurring them on to unlikely climaxes like someone with his wages on a horse. His rapport with 'Miami' Steve seems particularly warm on mike-sharing duties. Did two men ever get so close without exchanging oral fluids?

Their working of 'Reason to Believe' - Van Zandt on a white Teardrop guitar against the rattle of a snare, Springsteen coaxing some spine-chilling wailing noises out of a harmonica (has he got an animal in there?) - is powerful and moving, but he doesn't milk the applause, segueing almost impatiently into 'Darkness at the Edge of Town'. Clemmons steps forward to blow some blistering sax on 'She's the One', then it's the moment I've been waiting for - 'Livin' in the Future', my current favourite on the new CD. Needless to say, all these Spanish people already know every word of it ('Don't worry darling, hey baby don't you fret, we're living in the future, none of this has happened yet'). Bruce conducts the singing, then runs up the gangplank at the rear to visit the people who can only see the back of his head. 'Madrid - fantastico!' he shouts, then reads out an unflattering message in Spanish about America vis-a-vis Iraq. There follows the beautiful, elegiac 'Girls in Their Summer Clothes', my other new favourite. More than a third of the songs tonight are from the new album. This is no greatest hits show.

Of course he does 'Thunder Road' and 'Born to Run' - both of them more chrome-wheeled and fuel-injected than one would have thought possible. By now the whole place is bathed in full light, perhaps just to see what an ocean of swaying arms really looks like. Amazing is the answer, with sections of the crowd drawn like shoals of minnows towards the stage as he approaches, ebbing as he moves away. Scorsese is making a move too, perhaps for the last bus.

Bruce is finishing with one from the Seeger album, 'American Land', a rollicking immigrant jig with accordions and violin, a song of hope and opportunity, but also of betrayal and disappointment. Tonight, though, he has shown the knack of making everything seem possible.

· Bruce Springsteen and the E Street Band play one UK date, at the O2 Arena, London SE10, on 19 December. Returns only