Abraham, who scored 26 goals on loan at Championship Bristol City last season, announced his new deal on Twitter - although moments later the message was deleted.
He had written: "Happy to sign a new 5 year contract with @ChelseaFC."
Abraham has been linked with loan moves to Brighton, Newcastle and Celtic, but Swansea appear to have won the battle for his signature.
Swans boss Paul Clement used to be the Chelsea assistant boss.
It is normal practice for Chelsea's talented young players to sign contract extensions before departing on season-long loans.
Source : PA
Source: PA