The Baggies earlier confirmed the signing of forward Peter Odemwingie from Lokomotiv Moscow and Tchoyi's arrival after signing a two-year contract represents the end of another lengthy pursuit.
The 27-year-old Cameroon international has been on West Brom's radar fortwo seasons and he was finally given the green light to move to Englandby a review panel at the FA, who granted him a work permit on appeal.
Tough tackler: Midfielder Tchoyi (right) in action for Red Bull Salzburg
Unlike Odemwingie, Tchoyi will not be available for tomorrow's Barclays Premier League clash against Sunderland at The Hawthorns.
West Brom boss Roberto Di Matteo said: 'It's been a drawn-out process due to circumstances out of the club's control but all the hard work has paid off and I'm delighted to welcome Somen to the club.
'He is a powerful midfielder who will bring a physical presence to our team and also be a real threat at set-pieces.
'Somen has all the attributes to play in the Barclays Premier League but I think it is important we don't expect too much too soon from him as he will need a little time to adapt to English football.
'He also won't be sharp enough to be involved tomorrow as he has had to do a lot of travelling in the past few weeks which means he hasn't been able to train regularly.'
Di Matteo, meanwhile, is hoping Odemwingie's presence in the squad on Saturday, subject to international clearance, can provide a much-needed boost following last week's 6-0 thrashing by Chelsea.
Super Eagle: Odemwingie has a pop for Nigeria against South Korea
The 29-year-old, who has signed a two-year deal with the option of a further year, passed a medical and agreed terms last Friday and the deal was finalised the next day but Odemwingie then had to secure a work permit and visa.
Di Matteo said: 'I'm delighted to welcome Peter to the club. He is an exciting international, has a great c.v and I'm sure seeing a player of his calibre coming into the club will give everyone a lift.
'Peter has got great pace, is two-footed, scores goals and has good experience at a very high level. We've brought him in as a striker but he can also play out wide, which gives me options.'
Looking for a reaction: Baggies boss Di Matteo
Odemwingie was born in Uzbekistan and has dual Russian and Nigerian citizenship having lived in both countries as a boy.
He chose to play international football for the African nation and has scored nine times in 47 appearances, including Nigeria's only goal in their 2-1 defeat by South Korea last week.
The striker spent the last four seasons with Lokomotiv, netting 21 times in 70 starts, having previously played for Belgians La Louviere and French side Lille, with whom he gained Champions League experience.
Odemwingie and Tchoyi are Di Matteo's sixth and seventh permanent signings of the summer, following Steven Reid, Gabriel Tamas, Pablo Ibanez, Boaz Myhill and Nicky Shorey to The Hawthorns.
The Italian gave debuts to Tamas and Ibanez last weekend, and he will resist the temptation to make wholesale changes tomorrow despite their sobering experience at Stamford Bridge.
Di Matteo, who has already confirmed captain Scott Carson will keep his place in goal, said: 'There might be a couple of changes but not many. Scott knows he made a mistake and he is disappointed about it. But I have confidence in him and I would like him to show tomorrow that he can win us some points.'
The Baggies boss, meanwhile, is hoping his side can take advantage of the absence of Sunderland captain Lee Cattermole, who is suspended after picking up the first red card of the new Premier League season in their 2-2 draw with Birmingham last weekend.
He continued: 'It's going to be a tough game, but any team we face will be difficult to play. If we manage to cut out a few little mistakes that we made last weekend, we will give ourselves a chance.
'Cattermole seems to be an influential player so let's hope we can exploit that situation.'
Two players who will definitely not be available tomorrow are striker Ishmael Miller (thigh) and defender Joe Mattock (ankle), who have both been ruled out for up to a month after picking up injuries in training this week.
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