The Republic of Ireland U21 completed the formalities on the paperwork at the Ricoh Arena on Monday afternoon.
The Clitheroe-born 21-year-old was given his debut by Darren Ferguson against Scunthorpe United at Deepdale in 2010 and went on to make 60 appearances for the Lilywhites, scoring twice, including a memorable on live on TV against Burnley that same September.
Adam spent the latter part of last season on the sidelines, following a broken leg received against Walsall in February, however, he returned to fitness and completed the move to the Sky Blues on a three-year-deal.