Walsall have signed goalkeeper Neil Etheridge from Charlton on a two-year deal.
Brentford have confirmed the signing of FC Twente defender Andreas Bjelland.
The 31-year-old Baggies striker has 15 months remaining of his current four-year deal at The Hawthorns.
But, under article 17 of FIFA's transfer regulations, players over the age of 28 can end their contracts two years after signing for a club by paying a compensation figure determined by their wages and transfer fee.
Odemwingie tweeted: "I see a free player. A player who buys out his contract soon. Or a retired player. Does he look like he cares much? They made him not to."
Albion have already confirmed the Nigeria international will be dealt with internally after his Twitter attacks on the club on Sunday.
Odemwingie hit out at being only a substitute in recent games and for the club allegedly questioning his commitment.
Sources close to the Barclays Premier League outfit have indicated Albion will not sack Odemwingie, Press Association Sport understands.
Odemwingie is likely to face another fine after being hit in the pocket during January for a series of social networking outbursts.
But Albion will not ban the former Lokomotiv Moscow and Lille forward from using Twitter although any activity by players is governed by the club's disciplinary code of conduct.