Trolleys across the chain's 2,500 stores will have their locking systems disabled until they are adapted to accept the new coins.
See also: New 12-sided £1 coin to edge out old round pound
See also: Collectors' editions of new £1 coin on sale
A spokesperson for Tesco said: "We're replacing the locks on our trolleys to accept old and new pound coins as well as existing trolley tokens.
"As an interim measure we will unlock trolleys while this process is completed and we will continue to have colleagues on hand to attend trolleys in our stores, so our customers aren't affected by the changes."
Other supermarket groups such as Sainsbury's, Morrisons, Asda, Aldi and Lidl say their trolleys have been converted in time.
And it's not just trolleys the new multi-sided coins could cause problems for – parking machines and vending machines will be affected, and people are advised to keep both old and new coins on them.
The rollout of the new coins is happening because the existing coin has become increasingly vulnerable to counterfeiters.
They will cease to be legal tender on October 15, and any unspent coins can be changed at the bank, Manchester Evening News reported.
The rollout of the new £1 coin is happening Tuesday
The paper £5 note will no longer be legal tender from May 5.
Savers have been warned to use up their stash of old coins to make sure they are not left with currency that shops will no longer accept.