The former first minister told the Prime Minister “the British empire is over” as he hailed the SNP’s victory on Tuesday afternoon.
Downing Street has already said it will not permit a new separation vote to take place before the Brexit process has been completed.
However, speaking from Westminster in the wake of the vote, which saw 69 MSPs vote in favour of the SNP leader's plans, Mr Salmond blasted any attempts to try to disrupt the process.
He told BBC News: “Let me tell you the days of the British Empire are over, and the days of British prime ministers denying self-determination to the Scottish people are over as well.”
Alex Salmond issued a new warning to Theresa May over Scottish independence
Let me tell you the days of the British Empire are over
Mrs May has repeatedly told the SNP “now is not the time” to discuss ripping apart the 300-year union as Britain prepares to begin the complex process of leaving the European Union.
Following today's vote, a UK Government spokeswoman said: “We will not be entering into negotiations on the Scottish government's proposal.
"At this point, all our focus should be on our negotiations with the European Union, making sure we get the right deal for the whole of the UK.”
69 MSPs voted in favour of holding a new Scottish independence referendum
Mr Salmond rebuked the response, as he claimed the Scottish Government now had a “substantially clear majority for the people of Scotland to have the right to exercise their self-determination".
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He continued: “Theresa May may think she can stand against that, but she won’t be able to. Her position will come, not today, not tomorrow, but over the coming weeks and months.
“No British prime minister over the last generation has attempted to deny the Scottish people the right of self-determination.
“In my lifetime the biggest opponent of Scottish independence was Margaret Thatcher, but even Margaret Thatcher said in her autobiography that Scotland had an undoubted right of self-determination and if people were determined on it then no English politician would stand in their way.
“Theresa May, in taking the obdurate stance she’s doing, is attempting to deny the right of the Scottish people to decide.”
LIVE: Scotland reacts as Sturgeon gets her referendum Tue, March 28, 2017
A total of 69 MSPs voted to hold another referendum and 59 voted against
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Scotland's First Minister Nicola Sturgeon (R) reacts as she leaves the chamber following a vote on the second day of the 'Scotland's Choice' debate on a motion to seek the authority to hold an indpendence referendum at the Scottish Parliament in Edinburgh
Mr Salmond’s pitch was echoed by the Scottish mirst minister, who said it would be “democratically indefensible” for Westminster to try and block Holyrood's demands.
In a statement, she wrote: “We will now act on the mandate given to us by parliament by making a formal approach to the UK Government within the next few days after Article 50 has been triggered.
“This is, first and foremost, about giving the people of Scotland a choice on this country’s future.
“We know that Brexit threatens a hugely damaging and uncertain future for Scotland, and it would not be right if the people of Scotland – having been told in 2014 that the only way to protect our place in Europe was to vote against independence – were denied a choice.”