At the match in Flushing Meadows, N.Y., Becker used a big serve to send Agassi, a two-time Open champion into retirement with a 7-5, 6-7 (4-7), 6-4, 7-5 triumph at Arthur Ashe Stadium.
Agassi, 36, then accepted his retirement in tearful speech.
"The scoreboard said I lost today, but what the scoreboard doesn't say is what I have found," Agassi said on center court after the match. "Over the last 21 years I have found loyalty. You have given me shoulders to stand on to reach for my dreams. You have willed me to success even in my lowest moments.
"Over the last 21 years, I have found you and I will take you and the memory with me for the rest of my life."
Becker, 25, said Agassi had been his idol while he was growing up.