Stoke City have given Leicester City permission to speak to Robert Huth about a possible loan deal.
Ivica Olic looks to be on his way back to Hamburg, with Andre Schurrle increasingly likely to join Wolfsburg.
The 27-year-old, who almost signed for Swindon on deadline day, has agreed to move from south to west London after slipping down the pecking order at The Valley.
The deal will run until May 22, meaning Wright-Phillips will be available should the Bees make the League One play-offs.
Brentford sporting director Mark Warburton told the club website: "As we approach the business end of the season, it is very important to keep everything fresh.
"Bradley is a proven goalscorer in this division and is a player we have been looking at for a long time.
"He is a player who was chased by teams in the Championship and some of our rivals for promotion this season, so we are delighted we could secure him.
"We are very pleased to bring him to Griffin Park and hopefully he can help us achieve our aims and ambitions for the season.
"He had an outstanding season in League One last season and hopefully he can continue that form this time around."