The Healthscope board has recommended the bid in the absence of a superior proposal,and subject to an independent expert's report.
Investors may have to wait until as late as June for a meeting to approve the deal,which may leave time for a late return by rival suitor BGH-AustralianSuper,but the share price reaction on Friday suggested investors like the current offer.
Healthscope shares rose as much as 4 per cent to a high of $2.455 after the announcement before closing at $2.445. The formal offer on Friday would deliver Healthscope investors $2.465 a share,plus the 3.5c interim dividend.
Morningstar analyst Gareth James said the deal was becoming a forgone conclusion.
"From my perspective,it looks like the share price is closing in on the bid price now."
It is the highest the stock has traded since May last year when Ms Dwyer's board knocked back rival bids from Brookfield and BGH.
"When the bids got knocked back last year,I think that was a rude awakening for shareholders as to what the alternative might look like,"said Mr James.