The 28-year-old becomes Chelsea's seventh first-team signing of the summer following the arrivals of Hakim Ziyech, Timo Werner, Ben Chilwell, Thiago Silva, Malang Sarr and Kai Havertz.
Mendy is following in the footsteps of Petr Cech - now Chelsea's technical and performance adviser - who made the same move from Rennes to Stamford Bridge in the summer of 2004.
The 28-year-old kept nine clean sheets in 24 Ligue 1 appearances last season with Rennes, helping them to finish third and qualify for the Champions League for the first time in their history.
Mendy said: "I am so excited to be joining Chelsea. It's a dream for me to be a part of this exciting squad and to work with Frank Lampard and all of his coaching staff. I look forward to meeting my team-mates and can't wait to get started."
On signing Mendy, Chelsea director Marina Granovskaia said: "As soon as Petr Cech and our technical team identified Edouard as the most suitable goalkeeper to complement our existing group, there was only one player we wanted to bring in.
"Edouard arrives following a season of real success with Rennes, he is ambitious for more, and we welcome him to our club."
Kepa has started the season as Chelsea's first-choice goalkeeper but made a mistake for Brighton's goal in the Blues' 3-1 opening-weekend win and was at fault for one of Liverpool's strikes in the champions' 2-0 victory at Stamford Bridge on Sunday.
Carra: Kepa going through a nightmare
Lampard revealed goalkeeper Kepa had put his hands up and conceded he made a mistake to his teammates after Mane intercepted his pass to score Liverpool's second, and the Chelsea boss says rebuilding the Spaniard's confidence is now key.
However, Sky Sports' Jamie Carragher said the Blues' shot-stopper is in a difficult situation.
"As players, you go through tough times at different times in your career and you actually feel a bit sorry for Kepa now," said Carragher. "There's a new goalkeeper coming in so I don't think there's much more we can say about the goalkeeper.
"It must be tough for him and he's going through a really tough period. Our job is to be critical at times, but I remember when I went through a similar period earlier in my career. It wasn't going great and he's going through his own nightmare at the moment."
Neville: No top goalkeeper, no league title
Sky Sports' Gary Neville told Monday Night Football after Chelsea's win at Brighton:
"I don't think he [Lampard] is [happy with Kepa]. I wouldn't be. I know full well, having been in a coaching position, been in a changing room - you have to back your goalkeeper. You must back your players, you have to support them publicly. But privately, that goal... it's a really poor goal to give away.
"He conceded so many goals from outside the box last season, he's conceded another one tonight and it will cost you. If you don't have a top goalkeeper, you won't win that league.
"At this moment in time, he makes far too many mistakes. He lets too many goals into the back of his net that should be saved. 19 goals conceded from outside the box - that is a sorry story for a £70m goalkeeper.
"A few years ago, I used to be quite critical of Loris Karius and Simon Mignolet - 50 goals a season, but as soon as Alisson came, everything became normal. It was the same at Manchester United in my time, when we had that period between Peter Schmeichel and Edwin van der Sar. As soon as Van der Sar came, it became normal.
"Same with Manchester City in Pep Guardiola's first season. Claudio Bravo kept letting goals in from everywhere and the save-to-shots ratio was poor. As soon as Ederson comes in, everything becomes really normal.
"If you don't have your goalkeeper right, you are going to massively struggle to get where you need to get to. You certainly will never win a league."
Summer transfer window - key dates and times
The summer transfer window closes at 11pm on Monday, October 5 with a feast of activity lined up on Footy Legend.
A domestic-only window for deals between the Premier League and EFL then runs from October 5 and closes on Friday, October 16 at 5pm.
Source: Footy Legend