Former York forward Brodie, 25, spent last season on loan with Fleetwood, helping Micky Mellon's side to the Blue Square Bet Premier title.
"I have a year left on my contract at Crawley but I was looking to remain up north as I am settled here," Brodie told Morecambe's official website.
"There were several clubs interested in signing me but the gaffer just made me feel so comfortable. He is so passionate about the club and the game. It just felt right and I can't wait to get started.
"I have been here a couple of days and the lads have been fantastic. There is a real sense of togetherness and that will really suit me."
Shrimps boss Jim Bentley added: "This is a great signing for us and I am really looking forward to working with Richard. He is a goalscorer who always gives 100% and will fit in perfectly with the squad. He can play in several striking positions and will link up well with our forward players like Danny Carlton, Kevin Ellison, Jordan Burrow and Jack Redshaw."