Taylor is understood to have joined the company, set up by the former Prime Minister as an umbrella group for his business interests, late last month.
Before his six years at Morrisons Taylor spent three years as a policy officer for the Labour Party and another three years as a Ministry of Defence spad, all during Blair’s tenure as Prime Minister.
He also worked at public affairs agency Portland, which was set up by former Blair adviser and No 10 deputy press secretary Tim Allen.
Tony Blair Associates has been linked with controversial work undertaken by the New Labour architect, including advising Kazakhstan president Nursultan Nazarbayev, whose government has been condemned by Amnesty International over human rights abuses.
However Blair has reportedly argued that his commercial work has largely gone to fund charitable efforts through the Tony Blair Faith Foundation and Tony Blair Sports Foundation.
A spokeswoman for Tony Blair Associates confirmed Taylor’s hire but declined to comment on further details, including what role he will take.
His move comes as Morrisons battles critics after reporting a £176m loss last year, with the supermarket's founder Sir Ken Morrison labelling the current CEO Dalton Philips’ strategy "bullshit" at last week’s AGM.
Morrisons confirmed the departure and stated that Taylor's responsibilities would be split between head of comms Julian Bailey and head of corporate affairs Guy Mason.