The full-backs were both released at the end of the season but thoroughly enjoyed their spells with the Shrimps, in which time they won promotion to the Football League for the first time in the club's history.
Yates told the club's official website: "I have loved my time at Morecambe and I am leaving with a lot of fantastic memories.
Wembley was obviously a memorable moment in my career but there have been plenty more.
"It has been a great journey for the club and the fans who have always been fantastic to me."
And Howard added: "I have had a great five years at Morecambe and made a lot of good friends.
"Last year was a nightmare for me with a back injury but I am fit again now and I am just looking forward to playing football again on a regular basis. The medical staff at Morecambe were brilliant with me and looked after me superbly."