The TV journalist, 65, was first diagnosed with the illness in 2014 and again in 2017.
After having been off air due to his illness, Alagiah had been back on television on the BBC News At Six following his previous treatment.
A statement from Alagiah's agent said he "is to take a break from studio duties to deal with a further spread of cancer".
She added: "He was first diagnosed with stage 4 bowel cancer in April 2014. In a letter to colleagues in the newsroom Mr Alagiah said his medical team had decided to hit the new tumour 'hard and fast'.
"He is due to undergo a combination of chemotherapy and radiotherapy over the next few months.
"He added that working on the programme 'has kept me sane over the last few years' and 'I'm determined to come back'."
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.
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.