The Hammers have been trying to agree a fee with Lille for the midfielder, but have struggled to find success, with the French side not keen to sell.
Talks have been continuing between the two sides though and now West Ham have an agreement on a fee with the Ligue 1 outfit.
West Ham will pay €35m plus €5m in add-ons for Onana, according to French journalist Saber Desfarges.
The agreement means West Ham have been given permission to hold talks over personal terms with Onana and the discussions are taking place.
David Moyes will be hoping there are no hiccups along the way as he looks to complete the capture of the Lille man.
Onana was only signed by Lille from German side Hamburg last summer and is set for a quick exit from the club.
The 20-year-old made 41 appearances for Lille over the course of last term.