Did Buzz Aldrin say the eagle has landed?

No, the Commander, Neil Armstrong said it. From the mission transcripts:

102:45:40 Aldrin: Contact Light.

102:45:43 Armstrong (on-board): Shutdown

102:45:44 Aldrin: Okay. Engine Stop.

102:45:45 Aldrin: ACA out of Detent.

102:45:46 Armstrong: Out of Detent. Auto.

102:45:57 Duke: We copy you down, Eagle.

102:45:58 Armstrong (on-board): Engine arm is off. (Pause) Houston, Tranquility Base here. The Eagle has landed.

102:46:06 Duke: (Momentarily tongue-tied) Roger, Twan...(correcting himself) Tranquility. We copy you on the ground. You got a bunch of guys about to turn blue. We're breathing again. Thanks a lot.

102:46:16 Aldrin: Thank you.