He admitted he had considered making his own leadership bid, but said he had been impressed by current deputy leader Mr Fraser’s “fresh ideas and genuine vision”.
Mr Brown said: “Early on I had a number of nice messages from various people and of course I gave it consideration.
“Having reflected and listened carefully to what Murdo had to say, I was extremely impressed by his ideas, energy and what his vision is, so I’m giving him my support.”
A three-cornered battle is expected following Ms Goldie’s decision to stand down. As well as Mr Fraser, transport spokesman Jackson Carlaw has thrown his hat in the ring and new Glasgow MSP Ruth Davidson is expected to do so too.