The White Rabbit, the Cheshire Cat and Alice all feature in artist Grahame Baker-Smith's illustrations.
The story was made up by Charles Lutwidge Dodgson, a young don at Christ Church in Oxford, to entertain children on a boat trip in 1862.
It was published under Dodgson's pseudonym, Lewis Carroll, three years later.
One of the children on the Thames boat trip was Alice Liddel, the daughter of the dean of the college.
Alice later asked for the story, originally entitled Alice's Adventures Under Ground, to be written down. Dodgson did so as a Christmas gift in 1864 with his own illustrations.
It went on to become one of the best known works in children's literature, with numerous TV and film adaptations.
The stamps feature famous scenes from the book including the Mad Hatter's tea party and Alice falling down the rabbit hole.
Illustrator Grahame Baker-Smith said he had based the images of Alice on the stamps on his own daughter.
"The most difficult thing was consistency and working on such a very small scale. They all have to work as a set, so you want to have a range of colour and tone across the 10 stamps.
"The Royal Mail has a rich history of illustration on stamps, so the chance to have a go at that is a great opportunity."
Andrew Hammond, Royal Mail director of stamps and collectibles, said: "The story of Alice in Wonderland remains a perennial favourite of children, and indeed adults, around the world.
"It is fitting that in its 150th anniversary year it is celebrated with a wonderful set of stamps featuring striking images that do justice to such an iconic tale."

Krissoni Henderson accused Noor Alneaimi of being a prostitute and a non-believer, Birmingham Magistrates' Court heard.
He also called police officers arresting him "disgusting atheists".
Mr Henderson, 31, will be sentenced on Tuesday.
He had denied using religiously aggravated threatening words or behaviour.
More on this and other stories from Birmingham and the Black Country
Ms Alneaimi, 38, told the court she had heard the defendant shouting abuse at a passer-by on New Street, Birmingham, on 4 July before he turned to her and made a comment about her "tight" jeans.
"He directed the conversation to me and started saying you are a 'kafir' [an Islamic term for a non-believer]," she said.
"He said 'You shall burn in hell, look at your jeans they are so tight. You will burn in hell for wearing such clothes'."
Ms Alneaimi told the court she was "astounded and absolutely terrified" by his behaviour, leading to her filing a complaint with West Midlands Police.
Footage from cameras worn by officers visiting Mr Henderson's flat, on Brook Street in Birmingham, showed the defendant shouting at officers, including calling one a "filthy disgusting beast" and a "statue worshipper".
He also shouted "Allahu Akbar" before he was arrested, the court heard.
During his trial Mr Henderson said Ms Alneaimi may have "targeted" him and been trying to seduce him, saying she may have been attracted to his muscles.
Mr Henderson declined to confirm his religion, saying his beliefs are "to love people regardless of what they wear".
A set of 10 stamps is being issued to mark the 150th anniversary of Lewis Carroll's Alice in Wonderland.
[NEXT_CONCEPT]
A street preacher who told a woman she would "burn in hell" for wearing tight jeans has been found guilty of religiously aggravated threatening behaviour.