The striker has signed a five-year deal with Nottingham Forest, reuniting with former teammates James McAtee and Omari Hutchinson, whom he previously played alongside at Manchester City and Ipswich Town respectively.
Delap joined Chelsea from Ipswich last summer for £30m after the Tractor Boys' relegation triggered a release clause in his contract, but found first-team opportunities harder to come by at Stamford Bridge than during his prolific loan spell at Portman Road, where he scored 12 goals in the Premier League, two of them set up by Hutchinson.
"I'm buzzing. I really can't wait to get started, it's a massive club with a big history so I can't wait," Delap said. "I spoke with the head coach and I really like his way.
"I think he can be the one to really help me develop and get to that next step. There's some top players here as well and I'm looking forward to playing alongside them."
Delap is hoping to rediscover the form that made him one of the Premier League's most talked-about young strikers during his season at Ipswich.
"It was probably the time when I've enjoyed playing football the most and I think that was when I played my best football as well. Hopefully I can recreate that here," he said.
"I've spent a lot of time with Macca [James McAtee] and it's really helpful when you know people, and I had the year with Omari [Hutchinson] as well. I think those connections will definitely help with settling in. Macca is one of my best mates and I think we played really well together when we were younger, so I can't wait to be on the pitch with him once more."
The 23-year-old set out his ambitions for his new club, framing his own game as built around directness and intensity.
"I'm aggressive and I play with a lot of speed and aggression. Hopefully I can bring some goals here as well," he said. "With the new head coach I think we can build something really strong. The main aim is to challenge and be a top club in the Premier League."