The Nigerian forward has joined the Midlands side after eight years with Everton and Albion are believed to have splashed out £6million to acquire the 25-year-old on a three-year contract.
Anichebe netted three times against the Baggies during his Everton days and told West Brom's website: "I've scored a few goals against the club.
"There have been a few moments in my history that have happened against West Brom.
"I scored my first Premier League goal against West Brom and I scored here on New Year's Day two years ago, when my dad was in hospital.
"I seem to pop up with a goal against West Brom. They are key moments in my professional career so far and, because of that, something pulled me towards the club.
"Having been at Everton, which is my team, for so long, for me to leave there had to be a reason, some sort of connection.
"I felt a connection to come to West Brom and, as soon as I heard there was an interest, I knew I was coming here."
Sessegnon glad to be on board
The Baggies massively upgraded their striking options on deadline day because they also purchased Stephane Sessegnon from Sunderland for £5.5m.
The 29-year-old signed a three-year contract just before the window closed at 11pm, having flown in from Paris, where he had stopped off en route to meeting up with the Benin national squad.
"I'm happy to have closed the deal, because the day was too long," he said.
"West Brom play very good football and have good players so, for me, it's a great choice.
"The gaffer (Steve Clarke) said he wanted me because he wants to play more football, add more movement and create chances.
"I'm happy to sign for West Brom and I'm excited to start now."