Sir Tom, who played for his entire career with the Lancashire side, the forward made 433 appearances for the club between 1946 and 1960.
Sir Tom was born at his parents' home in the street next to the club's Deepdale stadium and went on to win 76 caps for England.
Nicknamed the "Preston Plumber" after completing an apprenticeship with his family's plumbing business, he was knighted in the 1998 Queen's New Year Honours list.
Preston North End tweeted: "Preston North End have been informed of the extremely sad news of the passing of Sir Tom Finney."
Lancashire FA said: "One of this great county's football legends has finally left the field of play. God bless you Sir Tom Finney and may you rest in peace. £RIP".
Former Scotland internationalist Kevin Gallacher said: "Sad news about Sir Tom Finney passing away, he's gone but will never be forgotten."
Sir Tom maintained links to Preston North End into later life, serving as the club's president.
The Deepdale stadium is currently located on Sir Tom Finney Way and the ground's old West Stand was renamed the Sir Tom Finney stand in 1995, with his image on its seats
A statue outside the stadium's National Football Museum depicts a famous image of Sir Tom splashing through a puddle during a game at Chelsea in 1956.
Former team-mate Bill Shankly, who himself made 297 appearances with Preston North End before going on to huge success as Liverpool manager, said that, if pressed, he would say Sir Tom was "the best player ever born".
Stanley Matthews, who is the only English footballer ever to be knighted while still playing, said of Sir Tom: "To dictate the pace and course of a game, a player has to be blessed with awesome qualities.
"Those who have accomplished it on a regular basis can be counted on the fingers of one hand - Pele, Maradona, Best, Di Stefano, and Tom Finney."
And Sir Bobby Charlton said: "Sir Tom Finney was one of the greatest footballers there has ever been - he was the type of player that people would travel a long way to see.
Current Preston North End striker and England international Kevin Davies tweeted: "Tonight we have lost a footballing Legend. A true gent and a loyal servant to his beloved PNE. RIP Sir Tom Finney".
Former Republic of Ireland international Kevin Kilbane said: "I'm proud to say I grew up on the same street as Sir Tom Finney. Very sad to hear of his passing".