Daniel Craig will reprise his role as the British spy, with the script penned by Oscar winner, John Logan.
Producers Michael G Wilson and Barbara Broccoli said: "We're really excited to be working once again with Daniel Craig, Sam Mendes and John Logan."
Bond 24 is due for release in the UK on 23 October 2015.
It will have its US release two weeks later, on 6 November.
Mendes, who directed the recently-opened West End musical Charlie and the Chocolate Factory, said he was "very much looking forward to taking up the reins again, and to working with Daniel Craig, Michael G Wilson and Barbara Broccoli for a second time".
He added: "I am very pleased that by giving me the time I need to honour all my theatre commitments, the producers have made it possible for me to direct Bond 24."
Skyfall made $1.1bn (??700m) at the worldwide box office. It was also the highest-grossing film of all time in the UK, earning more than ??94m from ticket sales in 40 days to beat the previous record holder Avatar, which made ??94m in 11 months.
Skyfall won two Oscars - singer Adele's theme song of the same name won best original song and there was an award for sound editing.
It was also named the outstanding British film by Bafta.
It was reported in May that Mendes had resumed talks with producers about directing the next Bond film, having previously ruled himself out due to other commitments.
Mendes is due to follow Charlie and the Chocolate Factory by directing Shakespeare's King Lear at the National Theatre in January 2014.
The last film-maker to lead consecutive Bond movies was former editor John Glen, who directed five films in a row between 1981 to 1989.

Carla McGurn, 20, had been accused of assaulting the two-month-old boy on various occasions between January and February 2015 at a house in Fife.
She denied the charge, which was found not proven by a jury after a trial.
Miss McGurn, from Burntisland, had been accused of assaulting the boy by seizing hold of him and shaking him repeatedly.
It had been alleged that she inflicted "blunt force trauma" to the boy's head and body by "means unknown to the prosecutor", and that the assault had been to the child's "severe injury" and to the "danger of his life".
Skyfall director Sam Mendes is to direct the 24th James Bond film, due for release in 2015, it has been announced.
[NEXT_CONCEPT]
A woman has been acquitted of assaulting a baby boy to the danger of his life.