Only 31% of Premier League players are eligible to play for England.
Spaniard would serve as back-up for Lionel Messi, Luis Suarez and Neymar.
Isaac Hayden joined Newcastle United on a five-year deal.
Georginio Wijnaldum was Newcastle United's top scorer in his debut campaign in the Premier League.
Georginio Wijnaldum was Newcastle United's top scorer with 11 goals in the 2015/16 campaign.
Moussa Sissoko earlier admitted that Arsenal are his dream club.
Georginio Wijnaldum played every single Premier League game in his debut campaign scoring 11 goals.
Georginio Wijnaldum is linked with a move to Liverpool, Tottenham and Everton this summer.
Moussa Sissoko impressed for France at the recently concluded Euro 2016 finals and is keen to move from relegated Newcastle United.
The Magpies are reportedly willing to sell the France midfielder this summer.
21-year-old leaves Gunners after just two appearances for first-team.
Mike Ashley's Sports Direct cuts bonuses and dividends after "disappointing" year
The Dutchman scored 11 goals and registered five assists for Newcastle last season.
Benitez initially claimed further signings would only occur if players left.
The midfielder is currently with the France national side at the Euro 2016.
Gayle becomes second signing made by Rafael Benitez during summer transfer window.
Norwich and Aston Villa take on Blackburn Rovers and Sheffield Wednesday respectively in their openers.
Sissoko says he has already decided to leave Newcastle this summer.
Newcastle midfielder Moussa Sissoko has admitted his admiration for Arsenal and will be available for £10m.
How you can invest in Sports Direct and Newcastle United.
Sports Direct boss will appear at Westminster on 7 June but only if MPs visit company's headquarters before.
The Gunners leapfrog their closest rivals and secure a first second-place finish since 2005 with thumping win.