The 19-year-old attacking midfielder joins the Saddlers on a season-long loan deal after impressing for the Canaries' under-23s last season.
He had previously caught the eye for Peterborough United, making 11 senior appearances.
“I am very delighted to be here. I am buzzing to get to meet all of the players, all of the staff and obviously the fans soon," said Clarke.
“The main thing for me is to try and get some minutes, to play against men and have the physical side of the game, but I really want to show the players, staff and fans what it is that I am capable of and hopefully win some games.
“I have had a bit of pre-season with Norwich, so that has helped me with my fitness and I have got my touch back, I have got my eye for goal again.
“Coming in at this time of pre-season will help me quite a lot and hopefully now I can just go straight into it.
“I am a player that just wants to get on the ball. I like to get into pockets, I like to score, I like to get assists. I am a winning player, I just want to win games.”
Clarke progressed through the academy ranks at Peterborough and was snapped up by Norwich last summer.
He got nine goals and three assists in Premier League 2 last season.
Walsall boss Michael Flynn has thanked Norwich chief Dean Smith – formerly of the Saddlers – for his help with getting the deal over the line.
"I am excited to welcome Flynn to the squad. He is a very talented player and he gives us that creativity in the final third," said the Walsall chief.
“He has a very good range of passing and he is very highly thought of at Norwich City.
“I would like to thank Dean Smith and Norwich City for helping us in bringing Flynn into the club. I am excited to work with him.”