This is a less firm agreement than the "confidence and supply" model of co-operation which had been previously talked about.
The Greens said that disagreements over transport was one of "the main reasons" why no further agreement could be reached.
But the party said it would be prepared to consider a more formal pact if the Scottish Liberal Democrats decide to take part in government.
Mr Salmond said the agreement, released in a signed statement, on co-operation between the parties would set the tone for the four years of the new parliament.
"The Scottish Greens represent a substantial body of opinion in Scotland, regardless of MSP numbers," he said.
"Their formula for co-operation across parties short of formal coalition is an excellent example of the consensus we are seeking to build in the parliament, and sets a positive tone for the incoming government."
This is not a 'confidence and supply' model - this is a model of no confidence and instability
Scottish Labour Party source
Green co-leader Robin Harper said the deal laid the foundations for a "progressive new politics" for Scotland.
The two parties, Mr Harper said, had agreed on issues including blocking nuclear power, tackling climate change and extending the powers of the Scottish Parliament.
But he told BBC Scotland: "Given the present situation that (the SNP) are going to be forming a minority government, it really didn't seem to make sense for us to tie ourselves closely into confidence and supply or into coalition, because we have serious reservations about many SNP policies, particularly their transport policies."
Talks between the Greens and the SNP were sparked following last week's Holyrood election result in which the Nationalists won 47 seats - one more than their nearest rivals, Scottish Labour.
A source close to Labour leader Jack McConnell, who remains first minister until a successor is elected, said: "Alex Salmond has been in discussion for five days and hasn't been able to persuade the Greens to properly support him.
"This is not a 'confidence and supply' model - this is a model of no confidence and instability."