The 22-year-old, who has been given the No. 9 shirt in west London, attracted strong interest from a host of top clubs, particularly Manchester United, who were keen on signing the ex-Manchester City man.
However, after scoring 12 Premier League goals last season, Delap believes Chelsea offer the best route to silverware.
“Growing up watching this club, I understand the stature of it and how incredible it has been over the years,” said Delap.
“I wanted to come here to win trophies. When I spoke to the club, everyone wanted to get back to the very top, and they have the quality and the players to do that.
“The hunger and desire to keep adding trophies, to take the club back to where it belongs, that is the main objective.”
The move to Stamford Bridge reunites Delap with Enzo Maresca, whom he worked with during his time at Manchester City.
Delap will compete with Nicolas Jackson for a starting spot as Chelsea's main striker.