The Blues announced both the new deal and the loan agreement for the 19-year-old, where he will join Swans boss and former Chelsea assistant Paul Clement.
"Happy to sign a five-year deal with Chelsea FC and also happy to announce I've joined Swansea AFC on a season loan," Abraham announced on Twitter.
Abraham spent last season on loan with Bristol City in the Championship and excelled, scoring 26 goals in 48 appearances for the club. He became the highest-scoring teenager in Championship history in the process, while scooping up Bristol City's Player of the Year and Young Player of the Year awards.
Happy to sign a 5 year deal with Chelsea FC & also happy to announce I've joined Swansea AFC on a season loan— Tammy abraham (@tammyabraham) July 4, 2017
The youngster will now aim to take his high-scoring ways to the Premier League with the Swans, who finished 15th in 2016-17 and spent most of the campaign staving off relegation.
Abraham has two Chelsea appearances to his name, both coming in the 2015-16 season.
The striker is Swansea's second signing of the summer after goalkeeper Erwin Mulder during their tour of the United States.