Fobert will take on the latest commission for the structure, which will house the art fair in October, following Adjaye, who had the commission for the last three years.
The Canadian-born architect said he was delighted to have won the commission, which follows his recent success winning a commission to extend the Kettle's Yard museum in Cambridge.
'Unlike permanent art spaces, this vast space must be constructed quickly and lasts for only four days,' he said.
'Frieze must function seamlessly both for its visitors and galleries, while also presenting a strong contemporary image of what an art space can be.
'I look forward to working with the Frieze team to find a solution to this challenge,' he added.