The pair have spent pre-season training at London Road and have shone sufficiently to earn contracts with the League One side.
Ireland was released by Barnsley after just one season at Oakwell, and saw a move to Darlington collapse earlier in the summer.
The Scottish defender has earned a two-year contract with The Posh while Kennedy has penned a three-year deal.
Kennedy, a Northern Ireland international, was axed by Wigan Athletic at the end of last term and had a spell on loan at Derby County last season.
Posh boss Barry Fry is confident the duo will prove to be valuable recruits during the coming season as Peterborough seek to improve in League One.
"Peter will give us the necessary balance to the team and is a great addition to the squad," Fry told the club's official website.
"Craig has agreed a two-year deal following his release from Barnsley and we are delighted to have signed him.
"We wish them both a very successful time at the club and they will certainly be good acquisitions for this football club."
