The former Bradford City and Sunderland boss replaces Dean Keates at the Racecourse Ground after the club failed to reach the National League play-offs.
Actors Ryan Reynolds and Rob McElhenney have picked the man they hope will help take them back to the EFL.
Parkinson, 53, knows the pressure is on to return the club to League Two after a 13-year absence.
He said: “Once the plans of the chairmen were explained to me, the decision to join Wrexham was very easy.
“Wrexham are an EFL club in all but the one thing that matters, league status, and we have a very clear objective with the work starting immediately.
“The club didn’t need selling to me, it sold itself and I wanted to be part of the journey this club is about to embark upon.
“We have a lot to do to be ready for August 21 and in the next seven weeks the aim is to add quality players to the existing squad, and create an environment and culture which gives us the best possible chance of promotion.”
Reynolds and McElhenney said: “We were presented with any number of good options, all of whom would have been very credible managers for the club.
“We’d like to thank all those that applied for the role but once we knew Phil was interested, he was our man and we got him.
“Phil has an immediate objective of gaining promotion but is conscious of our ambitions for the club and embraced each element of our vision.”
Wrexham were fan-owned since 2011 after the Wrexham Supporters Trust took control.
They voted overwhelming to rubber-stamp a takeover by Reynolds and McElhenney who pledged to invest £2m into the north Wales club.