The chic cabins, costing $76,500 each, have three outside windows, a small door and are clad in spruce shingles and plywood battens.
Ramsay is following celeb pals David Beckham and Guy Ritchie, who have both had "igloo-style" huts from the same Estonian suppliers installed at their country homes.
Theirs are saunas with a changing room attached, while Ramsay has the cabin version.
The chef's cabins, called the "Model 4", will be positioned facing each other at the bottom of the sizeable garden of the eight-bedroom Victorian home he shares with his Tana and their four older children Megan, 21, twins Jack and Holly, 19, and Matilda, 17.
The pods come with a fully functional kitchen, double bed, electric heating, a shower, storage, power points and a TV cable.
The council is yet to decide whether Ramsay, whose restaurants have been awarded 16 Michelin stars, will be given the green light for his family pods.
According to a planning application filed with the council on behalf of "G + T Ramsay", the "modest" structures will be almost nine metres long, just over two metres wide and almost two-and-a-half metres high.
No date has been set for when the Ramsay's planning application will be considered.
A council spokesman said: "This application will be considered on its merits in the usual way and any comments received will be taken into account when a decision is made."
If planning permission is granted, the council may well find itself receiving further applications as the sauna craze spreads throughout the Battersea glitterati. Nearby residents to the Ramsay household include DJ Johnny Vaughan, eighties pop star Simon Le Bon and comic Jack Dee.
He was inspired to buy the cabins after ex-England skipper David, 44, and his wife, Victoria, 45, forked out $27,000 on a triple sauna in a similar design at their $11.5 million Cotswold home.
Following its installation at the end of 2018, Beckham posted a picture on Instagram of himself relaxing on the terrace of the spruce shingle-clad bolthole with the caption: "Thank you to @iglucraft. I'm loving it with this cold weather right now."
The Beckhams apparently took the plunge with their Scandinavian steam bath after David had a go in Ritchie's hot room at the film director's 50th birthday party held at his country estate in Wiltshire last year.
Ritchie posted a photo on Instagram of himself and Beckham, dressed in a bathrobe, enjoying the sauna, which he jokingly captioned: "The sauna is brilliant. It is great to have a lake, a canoe, a waterfall and a husband with you."
Estonians are ecstatic that their love of a good sauna – which is much drier than a more humid Russian sauna or steamy Turkish experience - is now shared by British celebrities, with stories appearing in the country's media about the increasing devotion to their national pastime and Iglucraft.
And only last month, the growing garden sauna brigade was joined by EastEnders star Tamzin Outhwaite when she forked out $23,200 on a similar accessory at her $3.3 million home in north London supplied by the same manufacturer.
Tamzin, 48, who plays "Mel" Owen in the BBC Soap, opted for a design big enough to house her and toyboy, Tom Child, plus four more friends.