Leeds have reached a deal for Clotet to join the backroom team at Elland Road, reuniting him with their head coach.
Clotet worked as Monk’s number two at Swansea City and the Spaniard was identified by Monk as his first choice for the role at Leeds following his own appointment on June 2.
Clotet, a coach who never played football professionally, joined Swansea’s academy in 2013 while Michael Laudrup was manager but Monk promoted him to the assistant’s role after claiming the manager’s job the following year.
“He’s an excellent coach, a top calibre coach who brings a lot to the table and will help in the way that I work.
“He helps myself and will help all the players and all the staff and everyone at the club so he is definitely one of most importance.”
Flahavan, meanwhile, has returned to the club where he was briefly loaned from Crystal Palace in 2009.
The 37-year-old has retired from playing after a spell with Crawley Town last season and is a veteran of more than 400 Football League appearances.
He replaces Richard Hartis who joined Leeds as goalkeeping coach last summer but left recently to take up a job in the England youth set-up.
Flahavan did not appear for United during his short loan, acting instead as cover for Casper Ankergren and David Lucas.