This in turn led Takeaway.com to bump up its offer to 916p a share from 705p.
Takeaway initially agreed a takeover with the United Kingdom delivery company at the beginning of July. The increased offer was at a 25.6% premium to Just Eat's closing share price on 21 October 2019.
Dutch-owned Takeaway.com has triumphed in its bid for control of British food delivery firm Just Eat.
A statement from Prosus CEO Bob van Dijk thanked Just Eat's board and said his company's final offer had been "appropriate in light of the investment required" to make Just Eat competitive.
The combination of the two firms will create a delivery service worth around nine billion pounds ($11 billion) capable of competing against Britain-based Deliveroo and Uber Eats of the United States.
"We have been clear throughout that we would remain disciplined in how we allocate our capital and the price that we would offer", he said.
Earlier on Friday, Takeaway.com said its proposed all-share merger with FTSE 100 firm Just Eat has become unconditional as to acceptances.
While ending a colourful takeover battle, Takeaway's victory starts the hard task of integrating Just Eat.
But after a rejection from Just Eat, Prosus publicly raised its bid twice before Takeaway announced its final offer in December, valued at about 916 pence per share at the time.
The company said that the tie-up will result in annual cost-savings of around €20m (£17m), largely due to platform centralisation, better procurement, and the unification of branding.
As part of merger plans, Takeaway has said it is likely to sell Just Eat's 33% stake in iFood, Latin America's biggest food site, including its strong Brazilian subsidiary.
Prosus had argued it has the resources to make the significant investments in Just Eat necessary for it to stay competitive.
Prosus, the Dutch-listed consumer tech company which is owned by South African media titan Naspers, had offered 5.5 billion pounds ($7.1 billion) to buy Just Eat.