21-year-old Paterson began his career at both Coventry City and Manchester United before joining the Walsall Centre of Excellence.
Jamie penned his first professional contract in May 2010, and made his first-team debut as a substitute in the Johnstone's Paint Trophy fixture against Chesterfield in August of the same year. He went on to make his first start against Colchester in the following match and added several further appearances during the campaign, mostly from the bench.
Paterson went on to establish himself in the first-team, including starting every League One game last season.
Forest manager Billy Davies told nottinghamforest.co.uk: “We are delighted to have Jamie on board. He was very impressive for Walsall last season and has good pedigree.
“He’s quick, agile and has proven himself as a composed figure in front of goal. He adds another dimension to our attack.
“While Jamie is undoubtedly an exciting prospect, he has already gained good first team experience and that should help him make the step up to the Championship.”
The fee is believed to be an initial six-figure sum, rising to over £1,000,000 should Forest gain promotion to the Premier League, appearance clauses may also be included.