The veteran Scots MP won the job by just three votes last night in the Commons.
Lord Rennard, the former chief executive, is suspended from the party and is facing new internal disciplinary action for failing to apologise to alleged victims. He denies any wrongdoing.
Sir Malcolm, 69, added: "I'm obviously delighted. I thank my parliamentary colleagues for the confidence they have shown in me. What I was offering was experience and the recognition that the next 15 months are about reinforcing the economic message of what we have achieved in government - the £10,000 personal allowance, the triple lock on pensions and ameliorating the extremes of the Conservative Party - and what we can achieve in the next parliament."
LibDem leader and Deputy Prime Minister Nick Clegg said he was delighted by Sir Malcolm's election. He added: "He is admired across the party for his experience and his ability to keep a cool head; exactly what we need as we head towards the election."
The vacancy arose after Simon Hughes MP became Justice Minister.
Sir Malcolm has represented Gordon since 1983 and is due to stand down at next year's General Election and may move to the Lords.
Following hustings, he beat Burnley MP Gordon Birtwistle and then in the final round Solihull MP Lorely Burt, an aide to fellow Scot Danny Alexander, the Treasury Chief Secretary, by 28 votes to 25.
Some had suggested that victory for Ms Burt would demonstrate that the party was not hostile to women.
Posting on Twitter, Ms Burt wrote: "Not the result I hoped for but congratulations to @malcolmbruce … thanks to all supporters."
Sir Malcolm has served as his party's spokesman on Scotland, the environment, trade and industry as well as the economy, and is President of the Scottish LibDems.
He is currently chairman of the Commons International Development Committee, a post he made clear he wanted to retain.