Following Monday's decision by the TNS board to cave in and recommend the offer, 81.8% of shareholders had accepted it by 3pm yesterday.
This is above the 75% level at which WPP decided its offer would become unconditional to further acceptances.
Sir Martin Sorrell, chief executive of WPP, said: "We are delighted to be a step closer to welcoming such a fine company with strong people, clients and brands that will enhance our client offering."
Is the deal good for the market research industry? .
The majority of those who have accepted have chosen to sell their shares for 179p in cash and 0.1756 of a new WPP share rather than the WPP share-only option which offered 0.5471 of a new WPP share.
WPP has withdrawn the cash option for those who have yet to accept the offer, meaning they will only be able to take new WPP shares. The deadline for future acceptances is October 22.