The new terminal will feature a self-portrait of Lennon with the words "Above us only sky" taken from his classic anthem Imagine.
It will be called Liverpool John Lennon Airport when a new terminal opens in the spring.
This is the first time an airport in the UK will have been named after a famous person.
The former Beatle's widow, Yoko Ono, is due to visit the airport on Monday to be presented with a specially commissioned statue of the murdered star.
The new terminal will feature a self-portrait of Lennon with the words "Above us only sky" taken from his classic anthem Imagine.
A sculpture, commissioned from Tom Murphy, will stand inside the building.
Airport owners Peel Holdings saw the move as a "fitting and lasting tribute" to the murdered star.
Ono said: "As a gateway to the region this will be seen by millions of passengers and is a fitting tribute to the memory of my late husband."
The Beatles regularly used the airport on their travels in the early days of the band.
'Warmth and support'
The couple's son, Sean Lennon, said: "It is a great honour for my dad and for our family.
"My mom and I are very proud and would like to thank the people of Liverpool for all their warmth and support over the years."
And John's son Julian said: "I am very happy to see that Liverpool has taken the opportunity to remember one of its most famous citizens in a way that reaches millions of people.
"It seems that the name John Lennon will be around for a very long time - one way or another."
Lennon joins figures like John F Kennedy (New York), Leonardo Da Vinci (Rome) and Josef Strauss (Munich) who have had airports named after them.
He was murdered in his adopted city of New York in December 1980.