The Welsh club had already agreed an undisclosed fee with the Magpies and the 26-year-old will now undergo a medical on Tuesday before signing a three-year contract.
Swansea confirmed the news on their official website, www.swanseacity.net, on Monday afternoon.
Routledge will be joined in south Wales on Tuesday by Middlesbrough striker Leroy Lita, who will also undergo a medical after a deal worth £1.75million was reached with the Teesside club last week.
Should there be no complications, both players will come into contention for Wednesday's friendly against Celtic at the Liberty Stadium.
The pair continue manager Brendan Rodgers' summer recruitment drive following the arrivals of Danny Graham, Steven Caulker and Jose Moreira.
The much-travelled Routledge began his career with Crystal Palace before moving to Tottenham in 2005.
A broken foot curtailed his involvement at White Hart Lane and he moved to Aston Villa in 2008 after loan spells with Portsmouth and Fulham.
He then had another loan at Swansea's rivals Cardiff before moving to QPR and then Newcastle.
He returned to QPR on loan for the second half of last season and helped Neil Warnock's side clinch promotion to the top flight.
Source: PA
Source: PA