The Wales international, 28, arrives at the Liberty Stadium to boost Brendan Rodgers` options in attack after Marvin Emnes` return to Middlesbrough.
The likes of Matty Fryatt, Roman Bednar, Daniel Sturridge and even Eidur Gudjohnsen were all linked with loan moves to south Wales, but Easter is the man who will hope to provide a shot in the arm to the club`s promotion ambitions.
Easter has been absent with a thigh injury over recent weeks but is expected to start training with his new team-mates next week.
The Cardiff-born forward told Swansea`s official website: "I`m delighted to be here. My contract at MK Dons ends at the end of the season and I`ve made it clear that I want to play Championship football and have international aspirations. So the opportunity to come here was perfect for me."
Dons boss Karl Robinson added: "We`re disappointed to lose him. If he does well at that level then I`m sure there will be a number of clubs interested in signing him in January. If he comes back then he`ll do so knowing we gave him every opportunity to fulfil his ambition of playing Championship football."