Plaid Cymru leader Ieuan Wyn Jones said it was a "great honour" to become the Welsh assembly's deputy first minister.
He is Plaid's first government minister in the party's 82 year history.
In accepting the post as part of the coalition deal with Labour, Mr Jones said it was an "historic statement" personally and for his party.
Meanwhile, First Minister Rhodri Morgan is due to leave hospital later after his operation for partially-blocked arteries on Monday.
Speaking to the Assembly Members in Cardiff Bay, Mr Jones reached out to the two opposition parties, saying he was "very eager to see the new government acting in a mature way with consensus as a core element".
"I want to see the post-electoral spirit, of positive discussions between the parties, continuing throughout the third assembly."
He said it had been a "long journey" for Plaid Cymru.
"The party's role so far has been one of the opposition party which put pressure on the other parties to move things forward for the benefit of Wales," he added.
"From today we will be sharing the responsibility of directly operating on behalf of the people of Wales. I am looking forward to the challenge."
He said the One Wales document deal agreed with Labour reached the objectives of "creating an innovative and stable government, that would serve the people of Wales for four years".
Mr Jones was previously involved in coalition talks with the Liberal Democrats and Conservatives before the deal was reached with Labour.
"I truly hope that the discussions over the past few weeks will enable us to co-operate in several fields," he said.
Assembly Presiding Officer Lord Dafydd Elis-Thomas said of Mr Jones: "He's taken to the situation because he's got the experience and he's got the resilience to adapt to the new situation.
"I think he will be a very stable influence around the cabinet table in the difficult situation both parties are in now with the first minister's illness."
The identity and exact formation of the rest of the cabinet will have to wait probably until next week when Rhodri Morgan may feel well enough to finalise the negotiations he started with Plaid after Labour many weeks ago.
Mr Jones is expected to set out his broad ambitions for the coalition and will shoulder the responsibility of some of the first minister's duties.
The two leaders agreed the One Wales deal last month
His first public engagement will be alongside Health Minister Edwina Hart at the 90th anniversary of the third battle of Ypres at Passchendaele, in Belgium, on Thursday.
Mr Morgan, who is 67, was treated for two partially-blocked arteries after being taken ill over the weekend but is expected to leave hospital on Wednesday afternoon.
On Tuesday Mr Morgan's wife, the Cardiff North MP Julie Morgan said he felt "terrific".
"It was just lucky in a way it was detected now so he didn't end up having a major heart attack," she said.
"He thought it was an extreme gastric reaction - and certainly we all did until he had the last test which was taken 12 hours on."