The 30-year-old, who grew up as a United fan idolising Dwight Yorke and Andrew Cole, is set to join on loan for the remainder of the season.
“Odion is an experienced player. He will come in and give us an option of a different type of centre-forward for the short spell he’s staying with us,” Solskjaer said.
“A great lad and very professional, he will make the most of his time here.”
United are not believed to have the option to make the loan deal permanent for a player whose attempt to leave China earlier in the week was reportedly thwarted by the knock-on effect of the coronavirus outbreak.
Bowen has moved to Upton Park on a five-and-a-half-year contract for a fee understood to be around 20 million pounds ($39 million).
Hammers boss David Moyes was desperate to add some firepower to his relegation-threatened side, and is reported to have beaten Crystal Palace to the 23-year-old’s signature.
“When you score goals like he does, and in the numbers he does, in the Championship, it will give you a great chance of scoring goals in the Premier League,” Moyes told the club website.
Those deals came at the end of a quiet deadline day.
Arsenal were only other member of the English Premier League’s big six clubs to make a significant signing – the Gunners bolstering their defence by adding Southampton’s 28-year-old Portugal right-back Cedric Soares on a loan deal until the end of the season.
Manchester City defender Angelino, who has made 12 appearances for Pep Guardiola’s side in all competitions this season, has joined Bundesliga high-flyers RB Leipzig on loan with an option to buy.
Elsewhere, Liverpool and Chelsea bosses Jurgen Klopp and Frank Lampard ruled out any further activity before the window shut at 11pm (local time), while Real Madrid dismissed suggestions Gareth Bale could make a big-money return to Tottenham.
Lampard also quashed speculation that Olivier Giroud was set to leave Chelsea having been linked with a shock move to London rivals Tottenham.
Nineteen-year-old defender Tariq Lamptey has left Stamford Bridge, though, to join Brighton on a three-and-a-half-year deal.