Led by high-profile businessman Martin Sorrell, WPP clashed with Bain last month when the USA private equity firm announced plans to buy Japan's third-largest advertising agency for $1.35 billion.
On Tuesday it agreed to sell its ADK shares for 3,660 yen ($32.53) each, the same price it rejected last month.
It would then discuss an investment by WPP as a non-controlling minoring shareholder, according to a report in the Financial Times.
Like others, the Japanese market is undergoing a rapid transformation as money moves from traditional media outlets to digital.
The Tokyo-based agency, which is the third-largest in Japan behind Dentsu and Hakuhodo, claimed that the "expected synergies never fully materialised" between the two parties and that their partnership "simply no longer [made] sense".
"We are very pleased that WPP has shown its support for the privatisation of ADK", David Gross-Loh, Managing Director at Bain Capital Private Equity, said.
WPP would end arbitration and injunction proceedings if the tender offer succeeds, Bain said in its statement.
Bain has extended the offer to December 6 in order to seal the deal.