Downes is undergoing the second part of his Hammers medical this morning, having completed the first portion on Wednesday.
His signing could be confirmed as early as Thursday afternoon, with the fee for the 23-year-old potentially rising to £12m if add-on clauses are met.
Crystal Palace were at one stage believed to be leading the race for the Ipswich academy graduate, who is a lifelong Hammers fan, but failed to get a deal over the line before West Ham firmed up their interest.
Downes will become David Moyes’ third signing of the summer, after centre-back Nayef Aguerd signed from Rennes and goalkeeper Alphonse Areola made his loan move from Paris Saint-Germain permanent.
Following the retirement of club captain Mark Noble and the end of Alex Kral’s unsuccessful loan spell at the London Stadium, Moyes remains keen to sign another central midfield player in addition to Downes, in order to provide competition for Declan Rice and Tomas Soucek.
Meanwhile, the Irons are still waiting for Jesse Lingard to make a decision over his future, having made a firm offer of a return to the club.
Lingard is a free agent after leaving Manchester United at the end of his contract last month and enjoyed a superb loan spell at West Ham in the second half of the 2020/21 season, but has offers from a number of other Premier League clubs.