The 22-year-old, who began his career at Peterborough, had previously had a trial at Championship side Birmingham.
"Now that the deal is sorted my mindset has changed and I want to work just as hard at getting a place in the team," Brown told the club website.
"Having met all my team-mates during the trial, I know how competitive it will be to earn a place in the squad."
Cambridge head coach Shaun Derry added: "He's made a real positive impression on all of our staff. Technically he can more than hold his own within the group and he gives us further options in an attacking sense."
Meanwhile, Cambridge have confirmed that striker Adam McGurk has been placed on the transfer list.
Find all the latest football transfers on our dedicated page.​
Forward Jevani Brown has joined Cambridge United following a successful trial with the League Two club.