With a role to play in the race to finish in the top four of the Premier League, Tuchel led the Blues to the FA Cup and UEFA Champions League finals respectively.
Earlier this week, it was suggested that the Chelsea management position be happy to offer the German extension to his current 18-month contract.
With the acquisition of Solezwe, Abramovich will also give Tuchel the freedom to spend big money in the next transfer window as the club seeks to challenge Manchester City and its rivals.
Because of uncertainty about the future of Tammy Abraham and Olivier Giroud, Chelsea have been linked with Erling Haaland and Romelu Lukaku.
There could also be a new face in the middle of the pitch, an action that could allow Billy Gilmour to spend the season on loan at another Premier League club.