The former Bradford City man steps in after Mark Bower left the club at Tuesday lunchtime.
The ex-Morecambe, Scunthorpe and Wycombe attacker will combine the job of taking the team and lacing up his boots.
Avenue have finished in the top seven in the past two seasons - and another promotion push is wanted.
Thompson said: “I’m incredibly excited and can’t wait to get started. I’ve been working on coaching and looking towards my career after I finish playing. This is such a great opportunity at a fantastic club.
“I was attracted to the values and positivity of the directors and we agree on what a strong club requires in terms of attitude and culture.
“It’s fantastic to come back to Bradford, a city I’ve such great memories of the city.
“Bradford (Park Avenue) have been doing some really hard work and the contacts and support they have made available to us is impressive.
“I’ll be using every resource they’ve made available to me to achieve the best for the club.”
CEO Damian Irvine added: “It’s been an extremely busy 2019 for the club as we’ve focused on taking a fresh perspective and approach to every facet of our operation and structure.
“We have plenty of experience in seeing what successful and sustainable clubs look and feel like and it’s genuinely exciting to deliver positive change and a culture of progress to Horsfall Stadium.”