It means control over new machines with maximum stakes over £10 will be devolved, as the Wales Bill cleared its final hurdle in Parliament.
Shadow Welsh Secretary Jo Stevens wanted the power extended to existing terminals with maximum stakes over £2.
UK ministers expect the bill to gain Royal Assent in February.
The Wales Bill will hand Welsh ministers extra powers over transport, energy and electoral arrangements - including the power to increase the number of AMs.
It will also allow the Welsh Government to make some alternations to income tax.
But critics, including the Welsh Government itself, said other changes introduced too many restrictions on what it could or could not do.
On Tuesday, in the Commons, UK government amendments introduced in the Lords were accepted, devolving powers over water, fishing vessels and the right to be consulted over coastguard policy.
Welsh Secretary Alun Cairns said it was a "landmark day" and the bill "brings clarity to the settlement and accountability for Welsh Government".
In October, the UK government announced a review of FOBTs amid concern about their attraction to vulnerable people.
On the question of devolving FOBT regulation, a UK government spokesman said it was "giving Wales the same powers as Scotland has to address the local social problems that these machines can sometimes create".
Labour had claimed fixed-odds betting terminals (FOBTs) were highly addictive, allowing players to stake up to £100 every 20 seconds, compared to the £2 maximum bet on a fruit machine.
The party pointed to research showing there were four times as many betting shops in areas of high unemployment as in areas of low unemployment.
The Campaign for Fairer Gambling estimates that customers in Wales lost over £50m on FOBTs between September 2014-15.
The Association of British Bookmakers defended betting shops in Wales as the "safest place" to gamble as they were the most highly regulated retailer on the high street.

Officials said Mr Guelleh won 87% of Friday's vote, which activists complained was preceded by political repression and curbs on basic freedoms.
Mr Guelleh, in power since 1999, begins a fourth five-year term in power.
He faced five rivals in the election, but three opposition parties boycotted the poll.
The opposition complain of police brutality and media bias under Mr Guelleh's rule.
"The people of Djibouti have again entrusted me with the state's highest office," Mr Guelleh, 68, said in a speech on national TV.
More on this and other African news stories
Djibouti election: What you need to know
Djiboutiâ€™s thin-skinned democracy
Djibouti's strategic position on the Gulf of Aden means that it is home to US and French military bases.
The country is also seen as relatively stable in a region which includes Somalia, where the government does not control the whole country, and Yemen, where there is a civil war.
Observers say this explains the muted criticism of President Guelleh from the West.
Some 180,000 people were eligible to vote, around a fourth of the population.
The opposition were angry that the president rescinded his earlier decision not to seek another term.
His main rival, representing the opposition Union for National Salvation (USN) coalition, was Omar Elmi Kaireh, a Djibouti independence hero.
He came second, with 7%, according to provisional results announced by Interior Minister Hassan Omar.
A final attempt by Labour to give Wales more power to ban fixed-odds betting terminals has been defeated in the House of Commons.
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Djibouti's President Ismail Omar Guelleh has won a landslide victory in an election criticised by opposition parties and rights groups.