President Ibrahim Mohamed Solih took the oath of office in a unique and historic ceremony.
More than 300 foreign dignitaries from 46 countries were expected to attend the inauguration ceremony.
Yameen said he was respecting the wishes of thousands of supporters.
The four leaders met for the first time since September's election victory.
The former president will be the envoy of President Ibrahim Mohamed Solih.
Fainu islanders have been lobbying against the airport project.
Former speaker Shahid is expected to join the cabinet.
The whistleblower was declared an apostate after allegedly blasphemous videos were posted online.
Transition committees have been assessing ministries and state-owned enterprises.
The draconian law was abolished with 38 votes in favour and 13 against.
Velezinee is accused of mocking Islam, according to the arrest warrant.