The Central Scotland MSP defeated party health spokesman Anas Sarwar in a leadership vote triggered by the surprise resignation of Kezia Dugdale in August.
Mr Sarwar, MSP for Glasgow, was backed by several of the party’s high-profile politicians including MPs Ian Murray and Harriet Harman, while Mr Leonard had the support of trade unions.
Mr Leonard won the votes of 12,469 party members and supporters, while 9,516 backed Mr Sarwar. His election will help cement Mr Corbyn’s control over the Labour Party.
In his victory speech at Glasgow Science Centre, Mr Leonard said the result sent a “message of real change” and vowed under his leadership the party would be “distinctively Labour, confidently Labour”.
He immediately pledged “zero tolerance” of sexism, misogyny and sexual harassment.
“We need to change the political culture,” Mr Leonard declared, as he promised to set up an independent route for complaints.
Congratulating him on his election, Mr Corbyn said: “I am confident that under Richard’s leadership, Labour will once again be a real force for change in Scotland.
“This can be a turning point in Scottish politics and our party will now come together, united to challenge Tory and SNP austerity that has held Scotland back.”
Mr Leonard, a former head of economics at the Scottish Trade Unions Congress, was only elected to Holyrood last year and had the lower profile of the two leadership rivals.
The Yorkshireman takes the helm of a party showing signs of recovery in Scotland after slumping to just a lone MP in Westminster in the 2015 general election. Scottish Labour recovered seats and votes in this year’s election, while the SNP’s campaign for a second independence referendum has been firmly pushed back.
Announcing her resignation in August, Ms Dugdale said she left Scottish Labour “in better shape than I found it” and that a new leader with “fresh energy, drive and a new mandate” was need to take the party into the next Holyrood elections in 2021.
Mr Leonard’s victory on Saturday morning was partly overshadowed by a row over his predecessor’s decision to appear I’m a Celebrity... Get Me Out of Here!
Ms Dugdale, MSP for Lothian, was criticised by some party colleagues after it was reported she would fly to Australia to take part in the reality TV programme.
She will join contestants including boxer Amir Khan, Boris Johnson’s dad Stanley, and Saturdays singer Vanessa White in the jungle for the ITV show.
Labour MSP Jenny Marra tweeted: “Election to parliament is a privilege to serve and represent people. It’s not a shortcut to celebrity.”
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