Ex-Finance Minister Soumaila Cisse said he had congratulated Mr Keita and wished him good luck, AFP reported.
Mr Keita, 68, served as prime minister from 1994 to 2000.
Mali has suffered a year of unrest including a military coup and a French-led military intervention to oust Islamist rebels from the north.
No official results have yet been released following Sunday’s runoff, however, reports had put Mr Keita well ahead.
In the first round Mr Cisse polled just 19% against Mr Keita’s 40% and most of the other candidates then gave Mr Keita their endorsements.
Mr Keita – known as IBK – will now oversee more than $4bn (£2.6bn) in foreign aid promised to rebuild the West African state.
A 12,600-strong United Nations Stabilisation Mission in Mali (Minusma) is currently deploying, as France begins to withdraw its 3,000 troops.
After the first round Mr Cisse had complained of widespread fraud, with more than 400,000 ballots declared spoiled.
However, Mali’s Constitutional Court rejected the allegations and the head of the EU election observer mission, Louis Michel, praised the electoral process for its transparency.
On Monday, observers from the EU and the African Union again praised the way the second round was carried out.
“Malians should be congratulated because it seems to me they are regaining control of their democratic destiny, which is in fact nevertheless a tradition that exists in Mali,” said Mr Michel