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The former SNP Westminster leader won Edinburgh Central with a majority of 4,732.
He hailed his win as an endorsement of Nicola Sturgeon’s handling of the pandemic and support for Scotland’s right to choose independence.
"This result is an emphatic and unparalleled victory for the SNP in Edinburgh Central,” he said.
"The people – many of whom stood in queues during rain and hail – have spoken and their democratic choice has been to elect an SNP MSP in support of an SNP government dealing with Covid recovery, for the re-election of Nicola Sturgeon as First Minister and that Scotland’s future should be in Scotland’s hands.
"In this most European of capital cities, people have resoundingly rejected the party of Brexit and Boris Johnson. The public has rejected all the parties that want to block an independence referendum."
Mr Robertson said it was a huge honour to represent the constituency he grew up and all the communities of Edinburgh Central.
He said the constituency had its challenges, which he would do his best to address, and he named short-term lets hollowing out communities, the “scourge” of homelessness and drug-related deaths.
“I have pledged to work for Edinburgh Central and everyone who lives in it regardless of who they voted for and regardless of whether they voted at all,” he said.
Tory candidate Scott Douglas said despite his defeat, the Tory vote had increased.
“We managed to convince more voters this time than last time,” he said. “We didn’t manage to unite that unionist vote, but the SNP has had a huge increase in their support in the seat, which is disappointing, but there’s not much we can do about that.”
He said his party had finished a strong second, which showed people saw the Tories as the strongest opposition.
And he rejected the idea Mr Robertson’s victory should pave the way for another referendum.
"I still think there is majority support against independence on the whole, so I don’t think there is a need for another referendum,” he said.
"Just because the SNP have won this constituency doesn’t mean that the country wants it. And the people I have been speaking to over the last six months want to move on.”
Ms Davidson’s victory last time with a majority of 610 came as a surprise since the Tories had finished in fourth place at the previous election in 2011.
Tory insiders said the party’s Central Office had been more or less resigned to losing it as soon as she said she was standing down and little in the way of extra resources had been put into the campaign in the constituency.
Mr Douglas could not hope to compete in terms of name recognition with a high-profile national politician like Mr Robertson, sources said.
The Murrayfield councillor was a surprise choice as candidate and some Tories were saying long-serving City Centre councillor Joanna Mowat, who had been tipped to win the nomination, might have been a better bet.
But given the size of the SNP's majority, it may not have made much difference which candidate the Tories fielded.
Angus Robertson SNP 16,276
Scott Douglas Con 11,544
Maddy Kirkman Lab 6,839
Alison Jonstone Green 3,921
Bruce Wilson Lib Dem 2,555
Bonnie Prince Bob Independent 363
Tam Laird Libertarian 137
Donald Mackay Ukip 78
SNP majority 4,732
Turnout 62.69 per cent
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