The 21-year-old has been with the Baggies for almost 10 years but is now on the verge of a move to Portman Road, in a deal which could reach £1million if all clauses are met.
His impending departure will leave Albion with just two senior central midfielders in Jake Livermore and Romaine Sawyers, who both found themselves out of favour last season.
Harper, having progressed through the academy ranks, first broke into the senior set-up as a teenager in 2018/19.
He played 23 times that season and was subsequently linked with moves to both Tottenham and Norwich.
The box-to-box midfielder would later commit his future to the Baggies by signing a three-year deal, but over the last couple of campaigns, his career at The Hawthorns has stalled.
Harper made just 16 appearances across 19/20 and 20/21, and he spent the second half of last term on loan at Birmingham in the Championship.
League One outfit Ipswich are thought to have initially contacted Albion about the possibility of signing Harper on loan before being told a permanent deal could be done.
They are believed to have offered £500,000 up front, with various bonuses potentially doubling the fee.
Central midfield looks likely to be a priority position for the Baggies' next boss, with Michael Appleton the current favourite.
The only other current options are Robert Snodgrass – a wide man by trade – and youngster Tim Iroegbunam who made the bench on the last day of the season.
Meanwhile, Conor Gallagher, who played in central midfield while on loan from Chelsea last campaign, has been linked with a £15million move to Crystal Palace.
The Eagles were reportedly keen on landing Gallagher last summer, too, before he linked up with Albion and made 32 appearances, scoring two goals.