Kezia Dugdale spoke out after the veteran left-winger was re-elected to the post after defeating challenger Owen Smith, and called on MPs to now unite behind the leader.
After the result was declared, Mr Corbyn, who won 61.8% of the vote, told the Labour Party conference in Liverpool the party must now “wipe the slate clean”, adding that both he and Mr Smith are part of the “same Labour family”.
Ms Dugdale, who had backed Mr Smith during the campaign, congratulated the re-installed leader, and urged the party’s MPs to get back him, saying: “We can’t fight the Tories when we are fighting each other.”
The Scottish Labour leader, who has recently secured more autonomy for the party north of the border, said in a statement: “Congratulations to Jeremy for winning the leadership election.
“Hundreds of thousands of people across the UK took part in this election and the Labour Party is now the largest party in Europe.
• READ MORE: Jeremy Corbyn re-elected Labour leader
“We need to harness the energy and enthusiasm of our movement into real change for the people of the UK.”
She added: “Jeremy can unite the Labour Party, but he needs to want to unite it. That means he needs to work with both the party across the country and MPs to provide an effective opposition to the Tories in Westminster.
“It will be a difficult task for Jeremy, but not an impossible one. Likewise, the Parliamentary Labour Party must recognise that a divided Labour Party serves no-one.”
MSP Neil Findlay, who had led the Scottish campaign for Mr Corbyn’s re-election, hailed the “fantastic result” from the leadership ballot.
Mr Findlay, a former candidate for Scottish Labour leader, said: “If there was ever any doubt, the question of leadership and the political direction of our growing and invigorated party is now settled.
“We now need - all of us - to unify and rally behind that and be the radical alternative that is needed in Scotland and across the UK.”
That message was echoed by Pat Rafferty, the Scottish secretary of Unite, who said union members had backed Mr Corbyn “because they know that we need a different kind of politics and a different kind of economy in Scotland and right across the UK”.
Mr Rafferty added: “Jeremy’s campaign has brought together a movement of people united around the values of fairness, solidarity, respect and decency.
“Concentrating on those values will help us win power for working people and build a fairer society for all.
“Now that the contest is over, we look forward to people uniting behind Jeremy and opposing the austerity cuts that have been made in Westminster and handed on by Holyrood.”
But rival parties claimed Labour would still be bitterly divided, despite the ballot result.
Scottish Conservative leader Ruth Davidson said the election of Mr Corbyn would be “greeted with utter dismay by thousands of moderate voters across Scotland and the rest of the UK”.
The Tory said: “It is a sign of Labour’s utter mess that an attempt to get rid of Mr Corbyn has succeeded only in strengthening his grip on the party.
“This result now leaves Scottish Labour hopelessly divided.
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“Kezia Dugdale has repeatedly attacked Mr Corbyn in recent weeks but we know that her own deputy and many members of her team have urged the party to back him and his brand of hard-left politics.
“Mr Corbyn’s election means that, at both Holyrood and Westminster, Labour is simply incapable of providing a strong opposition to anybody apart from itself.”
SNP business convener Derek Mackay said: “Jeremy Corbyn should be congratulated for his victory - but it is unforgivable that Labour have overlooked their duties as official opposition at such a critical time to spend the summer tearing themselves apart.
“While Labour have been posted missing, the lack of clarity from the Tories on their plans to leave the EU has been a national scandal. Only the SNP have been properly holding Theresa May to account.
“And if Jeremy Corbyn can’t even convince his own leader in Scotland that he can become Prime Minister, how can anybody else take Labour seriously?
“This is a party that is completely and irreparably divided from top to bottom - and this division is the greatest gift the Tories could ever ask for.”
Mr Mackay added: “With the Tories seemingly determined to pursue a ‘hard-Brexit’ and Labour - by their own admission - completely unable to form a government for a generation, it is absolutely right that the First Minister keeps the option of independence on the table, to protect Scotland’s interests.”