The 19-year-old completed his season-long switch to the Swans on Tuesday afternoon, reportedly turning down the advances of newly-promoted duo Brighton & Hove Albion and Newcastle United to link up with Paul Clement's men.
Abraham, who put pen to paper on a new five-year contract at Stamford Bridge prior to being loaned out, is now looking forward to proving that he can make an impact at Premier League level following a profitable spell in the Championship with Bristol City last season.
"I'm really excited. I enjoyed my time at Bristol City last season, playing regular first-team football and scoring goals. Hopefully I can do the same at Swansea," he told the club's official website.
"I watched Swansea a lot last season when they played Chelsea and on TV. I know it was a difficult season for them at times, but you could see that they always try and play nice football.
"That was a major factor in me joining Swansea. When teams play good football it tends to create chances for the striker. Then it's up to me to get myself in good positions and hopefully score some goals."
Abraham scored 26 goals in 48 appearances for the Robins, while also registering once for England Under-21s during their run to the semi-finals of Euro 2017 this summer.