The MSP held the position during Ms Davidson’s recent maternity leave and is to step into her shoes after she quit for “professional and personal” reasons.
The party’s management board confirmed the appointment in a statement following a meeting on Thursday evening.
It said: “The management board of the Scottish Conservative and Unionist Party agreed unanimously that following the resignation of Rt Hon Ruth Davidson MSP as the Leader of the Scottish Conservative and Unionist Party on 29 August 2019, Jackson Carlaw MSP should be appointed interim leader of the Scottish Conservative and Unionist Party with immediate effect until the conclusion of the leadership election.
“The management board of the Scottish Conservative and Unionist Party will promulgate rules for a leadership election later this year to allow for the election of a new Leader of the Scottish Conservative and Unionist Party.”
Mr Carlaw, who became an MSP in 2007, is the current Scottish Conservative depute leader.
But having first stood for election in 1982, it is uncertain if he would want to take on the leadership role on a permanent basis.
A possible candidate to succeed Ms Davidson could be Murdo Fraser, who ran for the job against her in 2011.
At that time he proposed that the Scottish Tories should split from the UK party – an idea which could prove appealing given the lack of support north of the border for Brexit and Boris Johnson.
Adam Tomkins, the party’s constitution spokesman at Holyrood, could be another contender.
He was elected to Holyrood in 2016, but before that the constitutional law expert represented the Tories on the Smith Commission, the cross-party body which agreed the blueprint for greater devolution after the 2014 independence referendum.
Miles Briggs, meanwhile, has proved successful as Scottish Conservative health spokesman, pushing the Scottish Government to extend free personal care to under-65s as part of the Frank’s Law campaign.
Liam Kerr – another Conservative who came to Holyrood – has also been a strong performer as the party’s justice spokesman.
Ms Davidson has quit as Scottish Conservative leader earlier on Thursday.
aid leading the Tories in Holyrood – the job which she took on in November 2011 – had been the “privilege of my life”.
But as she formally resigned as leader, Ms Davidson – who had campaigned for Remain in the 2016 European referendum – cited the “conflict” she had felt over Brexit.
She clashed with Boris Johnson during the Brexit referendum, and her resignation came just a day after the Prime Minister announced he will temporarily suspend Parliament in the run-up to the UK’s EU departure date of October 31.
Mr Johnson paid tribute to her “wonderful service” to the Tories over the past eight years.
Additional reporting by PA.