Whyte left Crusaders in 2018 after playing a key part in the north Belfast side winning three Irish Premiership titles in four years.
He won Ulster Footballer of the Year award in 2017–18 before moving to League One side Oxford United.
After impressing at Oxford, the 28-year-old then signed for Cardiff City, but struggled.
He went out on six-month loan to Hull City, where he won promotion to the Championship, and had a year loan back at Oxford.
Whyte joined Portsmouth in 2023 and won promotion with Pompey before departing due to family reasons last summer, with a number of Irish Premiership and League of Ireland sides interested in securing his signature.
Coleraine boss Dean Shiels confirmed on Thursday that the Bannsiders were "interested" in Whyte but that he would be "really, really surprised" if a move materialised.
Lynch said that "every club in the country" was trying to sign Whyte.
"The plans that we put in front of him about what we want to do and where we want to go probably excited him the most", he told the club's website.
"He has played at the highest level and is the type of attacking player that gets people excited, which is what playing at the Brandywell is all about."
Whyte scored on his senior debut for Northern Ireland in September 2018 in a 3–0 win against Israel at Windsor Park and has managed four more goals in 30 international caps.
Boyce and Whyte join fellow Northern Ireland international Shane Ferguson at the Brandywell after he signed a one-year deal in December.
Under Lynch, who left Larne to replace Ruaidhri Higgins as boss in November, Derry have also recruited goalkeeper Arlo Doherty while Patrick McEleney, Will Patching, Daniel Kelly and Tadhg Ryan have left.