The Havre midfielder was on a target list the Gunners were to pursue this summer.
But the Hornets won the race for the 21-year-old who was out of contract this summer.
Watford has signed a pre-contract agreement with Gueye and he will officially travel to Vicarage Road on July 1 for a five-year contract.
This is despite the fact that the club is unable to give assurances about its prominent status as it faces relegation.
It will undoubtedly be frustrating for Arsenal if a team that could compete in the Championship next season beat them against the Frenchman.
Le Havre was sixth in Ligue 2, but its season ended Tuesday when the French Prime Minister said there would be no sport before September.
Gueye represented his country at U18 and U19 levels after signing his first professional contract in 2017.
This means that the Gunners will have to look elsewhere for midfielder recruits with Carlos Soler of Valencia, another name on their shortlist.
Funds could be higher in north London, although the Gunners are feeling the financial effects of the coronavirus pandemic.
The club is expected to prioritize free transfers and trade deals this summer.
This could hamper Mikel Arteta’s recruiting plans with the Spaniard eager to put his stamp on things.
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Its predecessor Unai Emery also suffered similar problems last summer on a minimal budget compared to its rivals.
That meant he had to be smart about how he had made deals with Nicolas Pepe’s club record move paid in installments.
William Saliba was allowed to stay in Saint-Etienne for another year of loan before traveling to the Emirates.