Mourinho had long stated that the window was closed for the Blues, having completed deals for Diego Costa, Cesc Fabregas, Filipe Luis and Didier Drogba earlier in the summer.
Fernando Torres' departure to AC Milan for the final two years of his five-and-a-half-year Chelsea contract - in effect ending his time at Stamford Bridge following his £50million move from Liverpool in January 2011 - necessitated the arrival of another striker, but even then Mourinho moved swiftly to sign Remy from QPR for £10.5million.
It could be if an opportunity arises - like the one last year which saw Willian join despite passing a medical at Tottenham - Chelsea may make a further signing, but, for now, Remy completes the squad for the first half of the 2014-15 campaign.
"I spoke with him (Mourinho)," Remy told chelseafc.com after agreeing a four-year contract.
"He is very clever and he knows exactly what he wants. He has targets for me and I know I have a target for myself as well.
"Everybody wants the best so the discussion was really good. I know he can get the best out of a player and I'm looking forward to working with him."
Costa has scored four goals in three Premier League games so far this season after his double in the 6-3 win at Everton.
Remy added: "We have two great strikers here already and I don't have a choice if I want to be in the team - I have to play at a very high level."
Many of those not in contention for a first-team place have left on loan - 21 in all after Marco van Ginkel, the midfielder who spent most of last season out with a serious knee injury, joined Torres at the San Siro.
The Dutchman's departure means Chelsea fulfil the Premier League's homegrown player rule and will have the maximum 17 foreign players in their 25-man squad.
Of the loan group, only Patrick Bamford, whose initial loan runs until January, did not leave on a season-long deal.