The Welshman, 48, who represented Great Britain's deaf swimming team in the 1990s, completed the crossing shortly before midnight on Sunday.
He was supported by his boat, the Louise Jane, and raised over £6,000 for the current Great Britain Deaf Swimming team after his 15-hour marathon.
The money will help deaf athletes, who receive little or no financial support, compete at the Deaflympics in 2017.
Don't let your deafness stop you
Andrew Rees' message to other deaf people after his swim
They have to raise the costs of competing for their country as well as training to be in peak condition for their events.
The 23rd Deaflympics are due to take place in Samsun, Turkey from 18-30 July, 2017.
After 18 months of long training sessions and preparations, Rees had set off from Semphire Hoe beach near Dover on Sunday morning.
For the first six hours, his stroke was fast and he was overtaking other swimmers, including those who were in relays.
But unexpected weather hit when he reached French waters, with gale force six winds creating 2.5-metre swells and making the waters choppy.
Nearing the French shores, swimming through jellyfish, Rees' next battle was the tide pushing him out to sea and at this point he was getting tired.
With light fading, communication became difficult due to his deafness - but he eventually crawled ashore at Sangatte beach around 11:30 BST.
Of the 11 support boats that had left that morning only two arrived.  The other boat was supporting a relay team that completed after Andrew.
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"I would like to congratulate Andrew on the fantastic achievement of completing the Channel swim solo, the first British deaf swimmer to do so," said GB Deaf Swimming's chair, Brian Baxter.
"This is a monumental coup, both on a personal level and especially for deaf and hard-of-hearing swimmers.
"We are very grateful that he nominated GB Deaf Swimming Club as the chosen organisation for fund-raising purposes.
"The money he has raised will help our Deaflympic swimmers immensely, and his swim will also serve as an inspiration to them all."
Referring to the first man to swim the Channel unaided, Rees said after his crossing: "Captain Matthew Webb's quote hits the nail on the head, 'Nothing great is easy'."
Andrew Rees has become the first deaf man to swim the English Channel solo.