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The longtime Rolling Stones frontman delivered on “I Can’t Turn You Loose” and then teamed up with Mr. Beck on “Commit a Crime.” Mr. Jagger got the president and his wife up out of their seats, swaying and clapping to the music, and picked up the pace with “Miss You,” performed with Shemekia Copeland and Susan Tedeschi.

Mr. Obama clearly was savoring the moment, closing his eyes at times and nodding his head as he lip-synced the words.

The president rose at the end to introduce the ensemble as the “White HouseBlues All-Stars” for the final song of the night, “Sweet Home Chicago.”

“For Michelle and me,” the president said, “there’s no blues like the song our artists have chosen to close with — the blues from our hometown.”

With that, the ensemble wrapped up the evening with “Sweet Home Chicago.” And then Mr. Jagger handed off the mic to MR. Obama for his presidential coda.

In advance of the concert, Grammy-winner Keb Mo had joked during a rehearsal break that Mr. Obama himself would perform, and there could even be a record in the works. He joked that Mr. Obama’s record would be called, “After the second term, now I can finally get my groove on.”

Maybe he wasn’t joking after all.

The lineup for Tuesday’s concert spanned multiple generations, from legends such as Mr. King and Mr. Guy to young faces such as 26-year-old Troy “Trombone Shorty” Andrews and Gary Clark Jr., whose style blends hip-hop, contemporary soul and indie rock. Also performing were Warren Haynes and Derek Trucks, with actress Taraji P. Henson as the program host and Booker T. Jones as music director and band leader.

The blues concert will be part of the “In Performance at the White House” series that airs on PBS. This one, designed to recognize Black History Month, will be broadcast on Monday on PBS stations and aired later on American Forces Network.