The band played an outdoor gig for 65,000 people Saturday in the same venue as a landmark 1969 show performed two days after the death of founding member Brian Jones.
It's most often remembered for the vast crowd of more than 200,000, for Jagger quoting Percy Bysshe Shelley as eulogy to Jones -- and for the white dress Jagger wore onstage.
Jagger took the stage in a similar white smock Saturday for a rendition of "Honky Tonk Women," a song the band also played in 1969.
"Just something I found in the back," he said.
Much else has changed since 1969. Then, the concert was free. On Saturday, some fans had paid 200 pounds ($300) a ticket. Jagger turns 70 this month, drummer Charlie Watts is 72, and guitarist Keith Richards is 69.
"It's taken a while, but we got back," Richards said.
And the Stones seemed genuinely glad to have returned. Fresh off a headlining slot at the Glastonbury Festival last week, the band was in relaxed but rousing form during a set that kicked off with "Start Me Up" and "It's Only Rock `n' Roll (But I Like It)."
"Anybody here that was here in 1969?" Jagger asked, getting at least a few affirmative shouts. "Welcome back -- it's nice to see you again."
The band played on a stage surrounded by fake trees and foliage --"like a cross between Wimbledon and a pantomime forest," Jagger said -- but it was scarcely necessary. The park was already a leafy idyll on a rare London day of bright sunshine and soaring temperatures.
"This time of year in England, it's the best place to be in the world," Jagger said, before quoting Shakespeare: "Summer's lease has all too short a date."
The show featured some songs that had yet to be written in 1969, including "Beast of Burden" and the recent "Doom and Gloom," as well as 1960s favorites like "Sympathy For the Devil," "Paint It Black" and "Gimme Shelter."
Former band member Mick Taylor, who played with the band for the first time at the 1969 show, joined the Stones onstage for "Midnight Rambler."
"We just found him in the pub and put him onstage in front of 200,000 people," Jagger joked of Taylor's debut.
The band nodded to its past with big-screen footage of old concerts, and saluted its inspirations with clips of blues greats from B.B. King to James Brown and Etta James. Young Texas bluesman Gary Clark Jr. was invited onstage to play with the band on "Bitch."
It all ended with fireworks and "Satisfaction" -- and for fans in the crowd, satisfaction.
"They're the greatest rock `n roll band in the world," said 25-year-old James Williamson, who inherited a love of the Stones from his father.
"At the end of the day, they're more talented than any band that's around today. They've still got an edge to them."
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