Roma will lose their top scorer from last season but need the money for Financial Fair Play reasons - and earning around £25 million for a 31-year-old striker is business that their sporting director Monchi seems happy with.
Dzeko scored 43 times in 55 appearances for club and country last term in all competitions and he comes in to challenge the misfiring Alvaro Morata. His arrival will also free up a loan move for Michy Batshuayi, who is thought to want to leave for Sevilla to play more minutes and ensure his place at the World Cup in Russia.
Antonio Conte is a fan of tall target men who act as a "pivot" or "focal point" for their attacks. Here's how the Italian head coach may use his potential recruit.
Dzeko's presence in this system could lead to Morata being benched as the Bosnian would take the No.9 role in the centre of the front three.
Chelsea require their central striker in this formation to occupy a couple of defenders and look to him to hit deep crosses to. Conte will also demand that Dzeko uses his ball skills and movement to play with the small, quick attackers that he would be lining up alongside.
Eden Hazard, Willian, Pedro and Charly Musonda would all challenge for the two outside attacker roles on either side of Dzeko. However, there is the chance that Morata could be utilised as a left-sided attacker, with Hazard on the right, a role that the Spaniard has played in at former teams.
The 3-5-2 has arguably taken over as Chelsea's main formation this season after the 3-4-3 proved defensively weak, especially in the absence of N'Golo Kante when he has been injured or rested.
Dzeko would only be playing alongside one other forward in this system, with Hazard taking on an increased responsibility as the team’s creator. The Belgian closes the gaps between defence and attack, while he's also needed to be effective on the counter-attack in a wide ranging role.
This system is used against the bigger teams and Dzeko must link up well with Hazard and the central midfielders who are charged with providing extra support in attack.
Chelsea are unlikely to start games in a 4-2-4 but have used it in the past while chasing matches. Conte considered using this attacking system when he first joined as he aimed to exploit the club's wide players but the formation he used successfully while coach of Bari proved to be too open.
However, this system could see Morata line up alongside Dzeko with two attacking wide men on either flank, which could cause problems for teams when Chelsea need a goal.
Morata would likely roam in this system with Dzeko, the less mobile of the two, acting as the focal point. Chelsea considered this formation last season in order to get the best out of Michy Batshuayi - alongside Diego Costa - but it never really got off the ground.