Murdoch, 23, has opted to join the Cod Army over other interested clubs and will complete the move, penning a two-year deal, when his contract at Falkirk expires at the end of June.
He made 40 appearances last season and scored six goals as the Bairns finished third in the Scottish First Division.
Fleetwood manager Graham Alexander said: "Stewart comes down from Falkirk and he's a lad we've been alerted to.
"We kept an eye on him, watched him a few times and spoke to many people up in Scotland and the responses were positive. I went to watch him myself towards the end of the season and everything I saw was great to see.
"I think he is a fantastic addition and it's a great opportunity for him to come to England.
"He can get up and down the pitch like a good old modern midfielder. We've seen the power he has and the way he can pass a ball. He ticks all the boxes.
"When I've spoken to him, you can see how dedicated he is to his job. He wants to do well because he is really ambitious and I think that's what he saw in us. He identified the journey the club want to go on and I think he really wants to be a part of it."