4:11PM BST 14 Jul 2011
The 32-year-old Iceland international is due to undergo a medical ahead of a move to Upton Park after he was released by Stoke City at the end of last season.
Premier League newcomers Swansea City were also interested in Gudjohnsen but he is set to sign a one-year deal to link up with West Ham and Sam Allardyce.
Gudjohnsen first came to prominence under Allardyce at Bolton 13 years ago, where he scored 27 goals in 77 appearances before moving to Chelsea for £5million.
He came close to signing for West Ham in January last year but at the last minute decided to join Tottenham, and subsequent moves to Stoke and a loan switch to Fulham saw him fail to find the net for either club.
Nevertheless, Allardyce wants Gudjohnsen to boost a forward line shorn of Demba Ba, Robbie Keane and Victor Obinna following the club's relegation and with Carlton Cole's future still uncertain.