Having paid a club-record fee of £5.5million for one striker on transfer deadline day in Stephane Sessegnon from Sunderland, it is understood Albion pushed the boat out further for Anichebe.
Although undisclosed, the suggestion is Albion splashed out £6million to land the Nigerian forward following an eight-year spell with Everton.
During his time with the Toffees, Anichebe scored three goals in seven matches against Albion, so when the club came calling he sensed a natural attraction.
"I've scored a few goals against the club," said Anichebe, on the club's official website.
"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; 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.
"For me, having been at Everton for so long, which is my team, 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."
- Sports & Recreation
- Stephane Sessegnon