Scharner has failed to trigger a 12-month extension option after making fewer than the required 25 appearances this season and is resigned to moving from The Hawthorns.
The Austria international has played a key role in the Baggies establishing themselves in the top flight.
Scharner said: "I think I've concluded my mission at West Brom by helping them to stay in the Premier League. I've never been relegated and I'm very proud of this.
"I didn't take up the (contract) option because it was impossible as I have not played enough games. To do so (stay) would need new negotiations - and that won't be happening.
"I would like to stay because of the supporters, who are great, but the club has other plans, so it is time to move on.
"But I think I still have enough to offer someone and have set myself a new challenge somewhere else. It is time to finish off the season and then decide on my future."