The couple had a shock victory over Tommy Fury and Molly-Mae Hague, who had been expected to take the title.
Greg won the £50,000 prize, and chose to split it with Amber.
Amber said she could "not believe it" after she and Greg won the dating show.
Greg penned a poem for Amber, in which he said he loved that she was "unique".
Amber replied that Greg had changed her experience at the 11th hour.
"You picked me up when I was at my most vulnerable and helped me to rediscover my smile," she said.
The victorious pair only got together in recent weeks, when Greg entered the villa as one of the bombshells.
A villa romance did not seem to be on the cards for Amber, after she was dumped by Michael Griffiths.
However, the 24-year-old rugby player took a shine to her, and she said they felt an "instant click".
After a recent date on a boat with Amber, Greg told the others: "That girl and that boat is just the stuff of movies."
During Monday night's final of the ITV2 show, he said he was looking forward to Amber showing him her home town of Newcastle.
When host Caroline Flack asked her what she saw in Greg, Amber replied that he had "nice energy around him".
"He's just lovely," she said.
Runners up Molly-Mae and Tommy said they were thrilled for Amber and Greg.
"Amber has had a hard time in here, she deserves everything that's coming to her," said boxer Tommy.
Molly-Mae and Tommy were expected to win the competition, after coupling up earlier on in the series.
Molly-Mae dissolved into tears as she thanked Tommy "for making me realise that fairy tales really do exist".
The boxer said she was everything he had ever wanted.
"You are my everything, my entire world and I'll love you until the day I die," he told her.
In third place came Ovie Soko and India Reynolds.
Ovie Soko and India Reynolds came third.
Ovie said he felt "great" as he had found "a wonderful lady".
He said he was looking forward to the pair taking their romance out of the villa.
The pair, who have only been together for 12 days, said a "family BBQ" was likely to be their first real date
In fourth place came Curtis Pritchard and Maura Higgins.
Maura said she could not believe the pair had made it so far in the competition
Dancer Curtis said his time in the villa had been "highs, lows and a lot of emotion".
He also addressed his split from Amy Hart, saying when they got together at the start of the series he had been caught up in a bubble and had not realised that there were "things missing" in their relationship.
He said Amy was "fabulous" and that although it had been hard, he owed it to her to be truthful.
Jack Fincham, the winner of Love Island 2018 alongside Dani Dyer, congratulated Amber Gill and Greg O'Shea for winning the 2019 series.
He said on Twitter: "Congratulations to Amber and Greg the winners of Love Island 2019."
Jack won the competition with his then-partner Dani Dyer.
They split up in December last year.
The series has been a huge hit, with millions of people tuning in for the couplings, dumpings and drama.
It was viewed by more than six million people at its peak this year.
It has been announced that next year the show will run for two series.