Of the 38 new appointments, 30 are from Labour, six are from the Tories and two from the Liberal Democrats.
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The new peers come despite Labour promising to reform the House of Lords.
A source told the PA that the Tories had created an “imbalance” that needed to be “corrected”.
Previously, there were 187 Labour peers compared to 273 from the Tories.
Ms Alexander took over from Jack McConnell as leader of Scottish Labour at Holyrood in 2007, after the party were defeated by the SNP.
Her time in charge was short-lived, and she resigned in 2008 amid a row over donations to her leadership campaign.
She has always insisted she acted on the written advice of the parliamentary authorities.
Ms Alexander, who represented Paisley North, most recently worked as Dundee University’s international vice-principal but stood down last month to take up a senior role with the British Council.
Her decision to quit came as the university warned of job cuts to plug a £30 million black hole.
Ms Curran, a former winner of The Herald’s Scottish Politician of The Year, has served in both Holyrood and the Commons.
She was Jack McConnell’s Communities Minister during her time in the Scottish Parliament and was Ed Miliband’s shadow Scotland secretary after she moved to Westminster in 2010.
The MP played a prominent role during the independence referendum and was a familiar face in the media. However, she lost her Glasgow East Westminster seat in the 2015 election to the SNP’s Natalie McGarry.
Ms Gray came to prominence in 2022 with the report into Partygate, she then became Sir Keir’s chief of staff in opposition before following him into Number 10.
However, she quit the role in October after a series of internal rows.
Others moving to the Lords, include former MP Luciana Berger who resigned from Labour in 2019 over the antisemitism scandal under Jeremy Corbyn. She rejoined in 2023 will sit on the Labour benches.
Mike Katz, the national chairman of the Jewish Labour Movement and Anne Longfield, who served as the Children’s Commissioner for England between 2015 and 2021 will also be made life peers.
Among the other Labour names on the list put forward by Sir Keir are former MPs Ms Debbonaire, Julie Elliott, Lyn Brown, Steve McCabe and Kevin Brennan, as well as former Welsh first minister Carwyn Jones.
Ms Debbonaire had served as Labour’s shadow culture secretary but lost her seat at the general election to the Green Party.
As well as Mr Young, the nominations from Conservative leader Kemi Badenoch, include Dame Therese as well as former housing minister Rachel Maclean, Oxford professor Nigel Biggar, former deputy mayor of London Roger Evans and Joanne Cash, a barrister and co-founder of Parent Gym.
Mr Young said he looked forward to working with Ms Badenoch to “restore free speech to pride of place in our democracy and repair the damage Keir Starmer has done to this vital human right when she succeeds him as our next Prime Minister.”
Sir Ed Davey’s nominations include Mark Pack who has been president of the party since 2020.
The SNP do not sit in the House of Lords.