The pair were appearing on RTÉ's The Saturday Night Show, hosted by Brendan O'Connor, when he got down on one knee and popped the question. Houghton accepted his proposal.
The couple, who have been dating since May, revealed on the show that they are seeking IVF treatment, prompting O'Connor to ask if he was going to propose.
"We're in Dublin," Reid said. "I haven't got a ring, but you know what, I'm going to do it. Seriously, nobody tell anyone! Will you marry me?"
They moved in together in August after declaring their love for one another. Both of them won Celebrity Big Brother in their respective years.
Reid is currently divorcing Katie Price, while Houghton was previously married to fellow Celebrity Big Brother star Samuel Preston.
> Chantelle Houghton: 'Katie Price was spiteful to Alex Reid'
Watch Alex Reid propose to Chantelle Houghton on The Saturday Night Show below: