The Glovers have wasted no time in finding a replacement for injured number one Stech, who broke his hand in the 1-0 loss to Birmingham on Saturday and could be out for three months.
Hennessey has accepted the chance to temporarily replace Stech at Huish Park and will finalise the move after Wales' friendly with the Republic of Ireland on Wednesday.
The 26-year-old, now fit again after twice damaging his cruciate knee ligaments, has not played in a senior fixture since initially sustaining the injury in April 2012.
He has been on the bench for Wolves' three games so far this season, and could make his Yeovil debut at Burnley on Saturday.
"After 18 months out, I am pleased that Wayne has been given the opportunity to go and play some first-team football," Wolves head coach Kenny Jackett told the club's official website.
"He has done all of the training sessions and has played in some of the pre-season fixtures but needs a regular run of games.
"It will be a good chance for Wayne to build up his match fitness, and is also in the best interests of the club to see him enjoy some regular first-team action."