But the 78-year-old Mujica can't say the same of Aerosmith, admitting after meeting with band members that he hadn't heard any of their songs.
The rockers met with Mujica in Uruguay's government house Tuesday, a day before Aerosmith's concert in Montevideo that is part of a Latin American tour.
The band gave the president a signed electric guitar. Frontman Steven Tyler said they consider Mujica one of the best presidents in the Americas.
"We believe in what he says," Tyler said. "Your president fights for freedom, and we also fight for freedom through music."
Mujica, a former leftist Tupamaro guerrilla, spent 14 years in prison and endured torture and solitary confinement.
As a politician, Mujica became known for his cantankerous personality, homespun oratory and insistence on keeping his life simple.
He still lives on a small, ramshackle flower farm with his wife.
His speech at the Rio-20 environmental conference last year urging simplicity in a world of conspicuous consumption has been viewed millions of times on YouTube.
After an unusually long, three-hour meeting with the band, Mujica posed for pictures with Aerosmith, smiling and holding his guitar.
He later said he'd raffle off the guitar and give the proceeds to a charity that provides poor families with the materials needed to build homes.