The 27-year-old Sweden international, who fired Sporting to the Portuguese league title last season with 39 goals and netted a Champions League hat-trick against Manchester City, is understood to have signed a five-year deal at the Emirates.
Gyokeres' transfer, which could end up costing the north London club as much as A$131 million with performance-related add-ons, takes Arsenal's close-season spending to the region of A$410 million.
He becomes Mikel Arteta's sixth summer signing and follows defender Cristhian Mosquera, midfielder Martin Zubimendi, goalkeeper Kepa Arrizabalaga, midfielder Christian Norgaard and forward Noni Madueke in moving to north London
Arsenal confirmed the news with a brief post on X which read: "This is where you need to be. Viktor Gyokeres is a Gunner."
Gyokeres will be expected to meet up with his new team-mates in Arsenal's ongoing pre-season tour of Singapore and Hong Kong.
The Gunners face Newcastle in the Singapore National Stadium on Sunday ahead of the concluding game of their tour, against Tottenham in Hong Kong on July 31.
Gyokeres moved to Brighton from Swedish side Brommapojkarna in January 2018, but spent time on loan at St Pauli and then Swansea and Coventry, before making a permanent move to the Sky Blues in July 2021.
After Coventry were beaten on penalties by Luton in the 2023 Championship final at Wembley, Gyokeres completed a $A42 million switch to Sporting. He scored a remarkable 97 goals in 102 matches for the Lisbon side.
Arsenal, who have finished runners-up in each of the last three EPL campaigns, spent the concluding months of last season without a recognised striker following long-term injuries to Gabriel Jesus and Kai Havertz.
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