Mr Boycott, 77, spent ten days in hospital in Leeds after having the operation at the end of last month.
He hopes to return to his job as a summariser on BBC Test Match Special in time for the third Test between England and India at Trent Bridge on August 18.
In a statement on Twitter, Emma Boycott, his daughter, said: “My Father, Geoffrey Boycott, had quadruple bypass open heart surgery on Wednesday 27th June.
“He spent 10 days in hospital in Leeds, with most of that time in the Cardiac Critical Care Unit.
“The surgeon says the operation was a success and has now allowed him home to recover from the invasive surgery.
“This will take some time so he will not be commentating at the start of the England v India Test match series but hopes to be back at work for the 3rd Test match at Nottingham.”
Mr Boycott, who has previously battled throat cancer with great courage and who remains one of the game’s most strident voices, was in good spirits at his home in Boston Spa.
He thanked well-wishers on Twitter and even found time via that platform to advocate Sir Gary Verity as the next chairman of Yorkshire CCC, following Steve Denison’s resignation yesterday in the wake of the BHS audit.
“Next Chairman of YCCC has to be @GaryVerity, he is clearly the best man for the job,” said Boycott of the CEO of Welcome to Yorkshire.
“He is honest, loyal, straight and with great vision and imagination.”
Replying to one comment in response to this, which said, “Shouldn’t you be resting Geoff?”, he quipped, “I am resting. I’m talking and Emma’s typing!”
Mr Boycott, one of the greatest batsmen in the game’s history, played 108 Test matches and scored 48,426 first-class runs, including 151 hundreds.