Dugdale, who has only been a Scottish MP for four years, beat veteran campaigner Ken Macintosh to replace Jim Murphy, who stepped down after his party lost all but one of their 41 seats to the pro-independence Scottish National Party (SNP), including his own seat on the outskirts of Glasgow.
Dugdale secured 72.1 per cent of the vote, which was open to around 21,000 party members.
"I know that the past few months have been incredibly difficult for Labour members across the country," she said on winning.
Read: David Cameron's Conservative party wins majority in British election
"But I have a message for Labour Party members... we are down but we are not out.
"I will work night and day over the coming weeks and months to make you proud, to honour that trust that you have put in me today, to give you some hope, to renew your faith in our abilities to transform the communities that we seek to serve," she added.
The SNP won 56 out of 59 seats in Scotland in the May 7 vote, in what was once one of Labour's strongholds.
Labour nationally is also searching for a new leader after Ed Miliband quit following a surprisingly big defeat by Prime Minister David Cameron's centre-right Conservatives. Voting began for the UK party leadership on Friday.
Left-winger Jeremy Corbyn is the shock favourite to take over, with other candidates including Andy Burnham, Yvette Cooper and Liz Kendall.
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