The 26-year-old will now discuss personal terms and undergo a medical at the Britannia Stadium with the deal expected to be finalised in the coming days, according to a statement on www.stokecityfc.com.
Kightly, who spent last season on loan at Watford, would become the Potters' second signing of the summer following Jamie Ness.
Meanwhile, Stoke striker Peter Crouch also thinks Michael Owen should join the Potteries outfit if he wants to enjoy playing regular football again.
Crouch has not looked back since leaving Tottenham to sign for Stoke for a club record ?10million deal 12 months ago, scoring 14 goals in 40 appearances.
The 31-year-old feels Owen would enjoy a similar lease of life if he signed up to manager Tony Pulis' squad, insisting it would not be a step down after being released by Manchester United earlier this summer.
"I know Michael has a big decision to make after leaving a club the size of Manchester United, but I had a similar decision to make last summer," Crouch told The Sun.
"At Tottenham we were challenging for a Champions League place every season. We're not doing that at Stoke, but we are building something worthwhile here. If you want to play regular football and enjoy playing again, this is a great place to be.
"I was really happy the manager could give me games when I was in and out of the Tottenham side.
"Coming to Stoke was never a step down. I'd rather play a big part in something smaller than be a small part of something bigger."
Source: PA
Source: PA