Mr Alagiah, who presents the BBC News at Six, was first diagnosed with the disease in 2014 and then again in 2017.
He had been back presenting the news since his last diagnosis but will now take a step back to undergo treatment.
The journalist is set to have a combination of chemotherapy and radiotherapy over the coming months.
“He added that working on the programme ‘has kept me sane over the last few years’ and ‘I’m determined to come back’,” his agent said in a statement.
Sri Lanka-born Alagiah underwent 17 rounds of chemotherapy to treat his advanced bowel cancer in 2014.
He returned to presenting duties in 2015 after making progress against the disease and said he was a “richer person” for it.
“I realised I wouldn’t give back a single day of the previous year’s experience,” he said.
“I wasn’t afraid of dying. I just wanted to get on with treatment.”
His cancer returned in December 2017, and the presenter underwent further treatment before once again returning to work.
Last year he tested positive for coronavirus after deciding to stop appearing in the studio during the outbreak following advice from doctors and colleagues.
Mr Alagiah joined the BBC in 1989 and spent many years as one of the corporation’s leading foreign correspondents before moving to presenting, and has hosted the BBC News at Six since 2007.
He was made an OBE in 2008 for his services to journalism.