The 25-year-old played for the Stones last season having previously been at Ebbsfleet, Concord Rangers and Braintree.
Crawley won promotion to the EFL by winning the National League in 2011 and have been there ever since.
Powell signs a two-year deal with the Red Devils who now play in the EFL League Two.
“We welcome Jack to the club. He has played at a good level for Millwall then dropped into the National League, which is where we were alerted to him," Crawley boss Gabriele Cioffi told the club's website.
“I like his attitude, he wants to do well, he wants to progress his career with us. He works hard, is creative in midfield and has very good energy levels."