Mr Cameron is scheduled to visit Scotland next week
The Scottish first minister has vowed to co-operate with new UK Prime Minister David Cameron when he "acts in Scotland's interests".
But Alex Salmond warned Scotland would not be a "helpless bystander" in the face of potential spending cuts.
Conservative leader Mr Cameron replaced Gordon Brown as prime minister after agreeing a coalition with the Lib Dems.
Scottish Tory leader Annabel Goldie said the new PM would repair relations between Holyrood and Westminster.
Mr Brown and his wife Sarah arrived at their home in North Queensferry, Fife, shortly before 2300 BST after leaving Downing Street earlier on Tuesday evening.
Mr Salmond paid tribute to Mr Brown as being "almost a force of nature" in Scottish and UK politics over the past 30 years, and said that "No-one could doubt his powerful intellectual capacity, his commitment, and the strength with which he pursued his objectives."
The first minister had previously called for a "progressive alliance" to be formed between Labour, the Liberal Democrats, his own SNP and Welsh nationalist party Plaid Cymru.
He claimed the Liberal Democrats would "rue the day" they instead agreed to a deal with the Conservatives, and predicted the party's voters in Scotland would feel "totally betrayed".
Mr Salmond told the BBC: "It is a great pity not just for Scotland but for people across these islands that the idea to change politics fundamentally wasn't grasped - it was a failure of political will.
"We have Scottish elections next year, we have a government in Scotland - we are no longer helpless bystanders in this as we were in the 1980s under Margaret Thatcher's government.
"We have secured the undertaking that there will be no changes to the budget which has been implemented in Scotland for this coming year and one of the partners in this new Conservative-Liberal alliance also gave us the undertaking that there would be no change to the funding formula.
"Obviously there is a new government in place in Westminster. Where they act in Scotland's interests we will co-operate. If they act against Scotland's interests, and that would include slashing our key public services in Scotland, then obviously they would expect us to resist that very strongly."
Mr Salmond said he would write to Mr Cameron on Wednesday in order to "set out some of the issues that the Scottish government regard as important in our relationship with the UK government" ahead of the prime minister's planned visit to Scotland next week.
The first minister added: "I congratulate David Cameron on the high office he has achieved, and will speak to the new prime minister at the earliest opportunity, and will of course welcome him to St Andrew's House during his planned visit to Edinburgh."
The Tories have only one MP in Scotland, but Ms Goldie, the Scottish Conservative leader at Holyrood, said Mr Cameron would treat Scotland with "respect".
She added: "The people of Britain wanted politicians to work together for the good of the country and David Cameron is committed to doing that.
"He is committed to repairing the broken relationship between our parliaments and our governments and he has said he will treat Scotland with respect. This is an opportunity to show that we can be a government for the good of all of Britain.
"I do not underestimate the scale of the task ahead, but nobody should doubt our resolve to take Scotland and Britain forward and to act in the national interest."
Labour's Scottish Parliament leader Iain Gray said Scottish voters would "pass judgement" on the Lib Dems for their "deal with the devil".
"Labour warned that a vote for the Liberal Democrats would only help David Cameron into Downing Street, and we were right," he said.
"The great majority of Scots rejected the Tories at the election and the Liberal Democrats will pay in the months and years ahead for propping up David Cameron."
Mr Brown left Downing Street after being unable to form a government
Former Scottish Secretary Jim Murphy MP said outgoing prime minister Mr Brown had made an "immense, impressive and substantial" contribution to public life" at home and across the world.
"Scots are proud of him, and proud of what he has done to make life better for those forgotten by others. He would not walk on by when others were in need," Mr Murphy said.
Last Thursday's UK general election resulted in a hung parliament, with no single party winning an overall majority of the seats at Westminster.
CBI Scotland's assistant director, David Lonsdale, said he was glad there had been a "timely outcome" to the post-election negotiations between the parties.
"What is needed now is an administration capable and willing to take firm action to eliminate the mammoth deficit in the public finances, and which has a convincing plan to rein in government debt and to pep up the economy particularly business investment and exports", Mr Lonsdale added.