Chris Coleman's side are on the brink of qualifying for Euro 2016 after beating Cyprus and drawing with Israel.
They will swap places with Chile, who are set to drop one to ninth spot, and remain above England, who will stay 10th despite two wins.
Northern Ireland, 41st in the current rankings, are expected to move above Scotland, currently 31st.
Had Wales beaten Israel, they would have risen to fourth but reaching eighth is still the sixth time in the last seven rankings that they have set a new record.
Argentina will stay top, while Germany will regain second place from Belgium, who drop to third.

The Ulster Unionist MP for Fermanagh and South Tyrone was elected in 2015 with DUP support.
MPs backed a request from the prime minister to hold a snap general election on 8 June by 522 votes to 13.
Sinn Féin's northern leader said Mrs May had shown a "blatant disregard for the people of the north".
Michelle O'Neill said the prime minister's announcement of a general election was about "the Tory party's self interest".
Meanwhile, the SDLP rejected any suggestion of her party entering a pact with Sinn Féin.
DUP MP Ian Paisley said the "deep frost button" had been pressed on power-sharing talks in Northern Ireland.
Mr Paisley expressed concerns about the future of the talks process during the general election campaign.
"We are seeing the freezer bags come out and the deep frost button being pressed on the Assembly," he said.
In the last general election, in May 2015, the Democratic Unionist Party (DUP) and Ulster Unionist Party (UUP) agreed pacts in four constituencies, including the UK's most tightly-contested seat of Fermanagh and South Tyrone.
That pact helped Mr Elliott take the seat from Sinn Féin's Michelle Gildernew - she had held on to it by just four votes in 2010.
On Tuesday, UUP leader Robin Swann said he was "open" to discussion on the issue of pacts.
Mr Elliott told the BBC on Wednesday it was important that the "people of Northern Ireland have representation at Westminster".
He also said talks with the DUP would take place in the days ahead to secure the "best agreement around some constituencies".
Earlier, DUP MP Sir Jeffrey Donaldson said his party wanted to "quickly" arrange talks with the UUP on a potential pact.
Sir Jeffrey told the BBC's Good Morning Ulster programme that the DUP was "prepared to go further" this time.
"We recognise that - if Northern Ireland is to maximise its representation and to have a strong voice in the absence of our own government - then we need to return MPs who will actually take their seats at Westminster," he said.
Sinn Féin currently has four MPs but they do not take their seats in the House of Commons, in protest at British rule in Northern Ireland.
Sir Jeffrey suggested there should be a new unionist pact in Fermanagh and South Tyrone and "other constituencies as well".
The DUP MP highlighted South Belfast as one constituency where the unionists could gain a seat from nationalists by agreeing to stand a single-unity candidate.
The  seat is currently held by SDLP MP Dr Alasdair McDonnell.
However, there will be no reciprocal deal between nationalist parties, according to Dr McDonnell's colleague, South Down MP Margaret Ritchie.
Mrs Ritchie told Good Morning Ulster: "We don't do electoral pacts".
"The SDLP fights the election - each and every election - on our own mandate and our own basis," she said.
Speaking on the same programme, Sinn Féin's national chairperson, Declan Kearney, said his party shared much "common ground" with the SDLP, Alliance and the Green Party on issues such as Brexit, equality and the legacy of the Troubles.
He said parties opposed to a hard Brexit and austerity policies should work together.
"We'll do our best to maximise the Sinn Féin vote," Mr Kearney said.
UUP MP Danny Kinahan criticised Sinn Féin abstentionism.
"At the moment, there are four seats where no-one turns up at Westminster and it is the mother of all parliaments," he said.
The UUP MP admitted that he was "likely to have a battle with the DUP" to hold on to his South Antrim seat.
He appeared to support a pre-election deal for Fermanagh and South Tyrone and potentially other seats.
Wales will rise to a new high of eighth when the next Fifa world rankings are released on 1 October.
[NEXT_CONCEPT]
The Ulster Unionist Party is to have talks with the Democratic Unionists about an electoral pact in the "next few days", Tom Elliott has said.