Koumas completes Baggies switch
The 22-year-old has signed a four-year deal as he sealed his £2.25 million move to The Hawthorns.
"Loads of clubs have had a look at Jason Koumas but no-one has taken a chance on him - until now," Megson told the club's official website.
"It's very similar to when we signed Jason Roberts and we're confident he can make a similar impact.
"This deal has taken a very long time to complete but we're delighted it's gone through.
"Jason can now concentrate on football issues.
"We haven't got his type of player at the club.
"Jason has bags of ability, good feet and can play in different positions across midfield. He's also got lots of experience for his age - but he has to learn to do more when he hasn't got the ball."