Mahathir and Anwar (a jailed reformist) won the general election last week.
He said some people were anxious about him taking the "bold" step but added: "I'm already 69 years old". He is now serving a five-year sentence on a second sodomy conviction.
He maintains his innocence, and says on both occasions Mahathir and Najib used trumped up charges against him to keep him out of politics.
Anwar had been scheduled to be released from prison on June 8, but the king agreed to grant him a royal pardon for an early release. He had been in hospital recovering from shoulder surgery.
The newly appointed 92-year-old prime minister also said Malaysia would reach out to Switzerland, the United States, Singapore and Luxembourg to return any 1MDB funds they may have received.
"I expect him to play the same role as the leaders of the other three parties".
Fernandes in a video released Sunday publicly apologized for supporting defeated Prime Minister Najib Razak, whose long-ruling coalition lost the May 9 election.
He said no final decision had been made on a Cabinet position.
Anwar's People's Justice Party (PKR), which has the most seats in the alliance, is demanding a proportionate number of posts in the cabinet.More news: Seattle City Council passes tax on big businesses
Wearing a white shirt printed with a photograph of Anwar and the words "March 2 Freedom", he said he nevertheless believed Anwar and Mahathir could work together and that the alliance's prospects were good.
Mahathir sacked Anwar as his deputy prime minister in 1998.
Supporters chanted "Reformasi" (Reform), the movement he launched two decades ago to challenge diverse Malaysia's race- and patronage-based politics.
"We are now in process of getting into details of matters he suppressed in his time", Mahathir said of Najib.
If found guilty, Najib faces up to 20 years in prison and a fine, legal experts said. If there is no case, we do not go for detention without trial. This included almost $700 million that landed in Najib's private bank accounts, the department said.
Anwar, who needs to contest a byelection to become a member of Parliament, said he doesn't want any Cabinet posts yet as he plans to spend time with his family and travel overseas for speaking engagements.
1MDB, set up in 2009 to fund domestic infrastructure projects and whose advisory board Najib once chaired, didn't submit management accounts for the year ended March 2015 and bank statements from foreign financial institutions.
The declassified report found, among others things, that 1MDB used 288 million ringgit ($73 million) of government funds to pay interest on its debt, which went against the monies' original goal.
A day later, photos of an AirAsia plane sporting the BN's campaign slogan "Hebatkan Negaraku" (Make My Country Greater) and colours was posted on Najib's Facebook page, which also show him boarding the plane with Fernandes.