London-born Lamptey, 21, represented England at youth levels while Williams, who was born in Bilbao to Ghanaian parents, was capped once by Spain.
Wing-back Lamptey had looked set to switch to the West African nation after asking to be left out of the England Under-21 squad for the European U21 Championship qualifiers last month.
The Ghana Football Association (GFA) expects their availability will help take the West Africans to the next level.
"The availability of these players means a lot to the Ghana Football Association and the technical team of the Black Stars," GFA president Kurt Okraku said.
"We have always maintained that we will not limit ourselves to only a small group of players but would scout top talents across the globe who are ready to sacrifice for the nation and to take us to the next level.
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