Mr Morgan has been pondering the cabinet's composition
First Minister Rhodri Morgan has announced his party will govern alone in the Welsh Assembly.
He told fellow Labour AMs he would not be seeking to form another coalition with the Liberal Democrats, who were partners for three of the body's four years.
Meanwhile, Plaid Cymru AM Dafydd Elis-Thomas was re-appointed presiding officer unopposed and independent John Marek was picked as his deputy, completing an unchanged trio of figureheads.
That gives Labour a slim but effective working majority to strengthen its hand in the second-ever assembly government at Cardiff Bay.
With two gains, Labour won 30 seats (half of the total 60) in last week's election - not quite an outright majority.
Coalition: Labour opts to govern alone
Figurehead: Dafydd Elis-Thomas presiding officer
Deputy: John Marek is his deputy
Cabinet: Rhodri Morgan names ministers Thursday
But, with Lord Elis-Thomas losing his regular right to vote, the balance of power is tipped 30/29 in Labour's favour.
Plaid Cymru and the Liberal Democrats wanted to see a Labour deputy elected - to redress the balance.
Labour AM and coalition critic Peter Law nominated himself for the post, while deselected Labour AM Mr Marek was put forward by Tory William Graham.
But independent Mr Marek won by 30 votes to 29 in a jovial secret ballot after Lord Elis-Thomas - to a round of applause - took his old seat at the helm of the chamber.
Mr Marek said: "I'd like to thank my friend Peter Law for a very close result - we will remain friends.
"I will serve the assembly to the best of my ability with integrity and diligence."
Rhodri Morgan was re-elected unopposed as first minister by a show of hands.
He said: "Whilst accepting that technically we do not have a majority we believe we have the confidence of people in Wales.
"We pledge ourselves to the service of the three million people who live in Wales."
Plaid leader Ieuan Wyn Jones called for a debate to review Labour's forthcoming policy programme.
The dismantling of the coalition will see the Liberal Democrats losing their two cabinet places - culture minister and rural development minister.
But Lib Dem assembly leader Mike German told Mr Morgan: "You have won the right to lead."
Mr Morgan is expected to reveal the composition of his new, all-Labour cabinet on Thursday.
The assembly will then convene on Tuesday, 13 May, at 1400 BST.
The Queen and the Duke of Edinburgh will officially open the second term of the Welsh Assembly during a Royal visit to Wales on 4 and 5 June.
It is also hoped that Prince Charles will accompany his mother, and will address the assembly in Welsh.