Osei has experience at Ware, Harlow Town, Grays Athletic, Enfield Town, Bishops Stortford, Margate and Hampton & Richmond Borough and has signed on non-contract terms.
Wealdstone manager Bobby Wilkinson said: “Jermaine is a talented young player and we will look at him over the next couple of months or so. He is hungry and wants to succeed and will be part of the squad at East Thurrock tomorrow.
“We are on the look out to add to the squad where we feel it is needed and we are working hard to bolster our striking strength. As you can imagine this is not easy at this stage of the campaign”.