Welcome Break hopes the new building will be open by Easter 2018.
It follows a huge fire that ripped through the service station in December 2016.
Fire crews from across Surrey and Hampshire rushed to the blaze on December 14 at around 10.30pm which left part of the service station in ruins. No one was injured.
A large temporary building opened on March 23 and houses a Starbucks, a small Waitrose, Burger King, Harry Ramsdens, WH Smith, Chopstix and a Starbucks Drive Thru.
It will remain in place until the new building is up.
A planning statement submitted with the application said the facilities in the proposed replacement amenity building are very similar to those destroyed in the fire.
“The main difference being that the new building allows for a modern layout which will be light compared with the darker, more cramped facilities that previously occupied the site,” it adds.
'Bold new design'
“Prior to the fire the existing amenity building at Fleet was of unremarkable design and, despite having been extended, was of an aged appearance with limited energy efficiency measures.
"The need to now replace the building in the wake of the fire therefore represents an opportunity for a bold new design that meets contemporary building standards. This will ensure that the services are fit for modern needs and attractive for visitors.”
The planning statement said the building has been designed to reflect the service area, which is surrounded by mature pine trees.
“Tall, slender columns produced from single trees will support the floating roof structure under which the service area facilities will be housed,” the statement says.
“The structure is a mixture of glass with timber panelling and blockwork."
“Architecturally it is considered that the new building represents a contemporary addition to the site with its use of fountains and timber supporting columns lending it a natural appearance.
“The proposals will clearly create an iconic and high-quality building.”
Welcome Break CEO Rod McKie said: “The redevelopment project at Fleet is very important to Welcome Break as well as the local community.
“The services are surrounded by the woods and it is our intention to blend the new-look building into the wonderful landscape that surrounds it.”
Hart will determine the application by July 8.