The striker was strongly linked with a move to the Blues in January, with manager Antonio Conte keen to strengthen his options at the top end of the pitch. Eventually, Chelsea landed Olivier Giroud from Arsenal.
"I really enjoyed the interest of Chelsea, a club I respect and appreciate," he said. "In the last few weeks, so many stories have been told about my departure from Rome, and I am still here today. Finally, I'm happy to stay in Rome, because it became my home and an incredible part of my life, life in an almost unreal way."
The striker has been a big hit for Roma since his arrival, initially on loan in 2015, having earlier scored consistently during a stint with Manchester City in English football.
As the Tifo Football Twitter account noted, the Bosnia and Herzegovina international is constantly making things happen in the final third:
The 31-year-old would have been an ideal fit for the Blues, and he boasts a lot of the qualities Conte typically wants in his centre-forwards.
Dzeko offers a tremendous presence at the point of the attack. He can pin back defenders, win aerial battles and bring team-mates into the game. Factor in that he's mobile and able to finish different types of chances, and he would have been a tremendous signing for Chelsea.
Roma will be delighted the striker ended up sticking around, and he will remain a key man at the Stadio Olimpico.
According to Matt Law of the Daily Telegraph, the striker also wanted Chelsea to break their policy when it comes to dealing with players over the age of 30:
In Giroud, Chelsea have signed a proven Premier League striker and someone who has many similar attributes to Dzeko. With Alvaro Morata struggling for form and fitness, it will be fascinating to see what type of role he plays in the coming weeks.
Dzeko, meanwhile, will be tasked with refocusing on Roma and helping them secure UEFA Champions League football for next season. The Giallorossi sit in fifth place in Serie A, with their star striker having netted 10 times in the competition.