Scrum-half Will Cliff, 23, and centre Jordan Davies, 21, will move in the opposite direction.
Titterrell, 30, was a Premiership winner with the Sharks during his first spell at the club between 2000 and 2007 and will move back to Edgeley Park on loan until the end of January, when he will return to Leeds Carnegie ahead of the Championship play-offs.
Cliff and Davies will join up with Leeds Carnegie with immediate effect for the remainder of the season and could be part of the squad for this Saturday's final pool game in the British & Irish Cup game at Pontypridd.
Commenting on the new arrangements, Leeds chief executive Gary Hetherington said: "This is not a decision we have taken lightly as Andy is a huge part of our club and where we want to be in the future.
"However, we recognise the fact that we have an excellent relationship with Sale and the fact that Andy would have no interest in playing for any other Premiership club other than the Sharks, who he still has a close bond with.
"We already have Tommy Bell and Iain Thornley on loan from Sale for the entire season and both players have been outstanding for us and the addition of Will Cliff and Jordan Davies will strengthen our squad in key positions for our promotion push in the New Year."
Titterrell, who made 122 Premiership appearances for the Sharks in his first spell at the club, is looking forward to the challenge of playing in the top flight again this season. He added: "This was a very difficult decision to make because we are building something special at Leeds Carnegie.
"However, I know the relationship with Sale is an important one for the club and I am looking forward to returning to the Sharks until the end of January. We have always said that our focus is on finishing the season strongly at Leeds and hopefully I will be able to contribute on my return as we look for our immediate promotion back to the Premiership.
"I go to the Sharks safe in the knowledge that we have got good hookers at Leeds Carnegie in Scott Freer, Phil Nilsen and Harry Hannan and I will certainly be keeping in touch with the guys whilst I am away however playing wise my immediate focus will be on doing my very best on the pitch for Sale."
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