And the governing body has revealed Ibrox Stadium will be the venue for both of the semi-finals.
Hampden is unavailable due to redevelopment work ahead of the 2014 Commonwealth Games in Glasgow.
Celtic Park is the country's largest stadium with a capacity of 60,355 and will stage the final on Saturday, May 17.
The semi-finals will be played at Ibrox, which has a capacity of 51,082, on Saturday, April 12, and Sunday, April 13.
Celtic Park played host to the Scottish Cup final between Hearts and Rangers in 1998.
The Hoops are the current holders of the Scottish Cup having beaten Hibs 3-0 at Hampden Park in May.
The SPFL League One match between Rangers and Ayr United, scheduled for Saturday, April 12, will be moved to a new date.
SFA president Campbell Ogilvie, said: "We are fortunate in Scotland to have three world-class football stadia.
"With Hampden due to undergo redevelopment work ahead of the 2014 Commonwealth Games, it is natural we would seek to utilise both Celtic Park and Ibrox as venues for Scottish football's premier cup competition.
"On behalf of the SFA, I would like to thank both Celtic and Rangers, as well as the SPFL, for their support in hosting these matches."
Celtic chief executive Peter Lawwell, said: "We are delighted Celtic Park has been chosen to host the William Hill Scottish Cup final.
"As we have seen this season, Celtic Park continues to be one of the finest stadia in European football, producing an occasion and an atmosphere like no other - we are sure our stadium will provide a brilliant setting for our national cup final.
"Clearly, Celtic are cup holders and I am sure manager Neil Lennon and the team will be doing all they can to ensure that we go as far as we can in the competition and hopefully be part of this great final at the end of the season."
Rangers finance director, Brian Stockbridge, said: "We are delighted Ibrox Stadium has been chosen to host the Scottish Cup semi-finals in April.
"The Scottish FA's decision to play these ties at the home of Scotland's most successful club underlines the fact that Ibrox remains one of European football's elite arenas.
"Of course, we hope to travel far in this competition ourselves but, no matter who plays at Ibrox, they can be certain of the warmest of welcomes."