West Ham also signed England striker Danny Ings from Aston Villa on Friday, while New Zealand international Chris Wood, at the moment surplus to requirements at Newcastle, has been snapped up on loan by Nottingham Forest.
Trossard's move to the Gunners, though, was the biggest move, just a week after Arsenal had missed out on their long-time transfer target Mykhailo Mudryk, who went to rivals Chelsea instead.
Arsenal have landed the 28-year-old Belgium winger Trossard for an initial fee of £21 million ($A37 million).
He adds to Arsenal's attacking options in the absence of Brazil forward Gabriel Jesus, who injured a knee at the World Cup, and joins after the Gunners were unable to lure the 22-year-old Mudryk.
The 24-times capped Trossard was described by Arsenal boss Mikel Arteta as a "versatile player with high technical ability, intelligence and a great deal of experience in the Premier League and at international level."
Arsenal hope the transfer documents for Trossard will be completed in time for him to be available for the game against Manchester United at home on Sunday.
The 30-year-old Ings, Villa's leading scorer with seven goals this season, has joined the Hammers for a reported fee of 12 million pounds ($A21 million) and should be eligible to play Saturday when West Ham host fellow strugglers Everton.
Villa had earlier this week reached an agreement to sign Colombia striker Jhon Duran from Major League Soccer team Chicago Fire for a reported $US18 million ($A26 million).
Wood is Forest's 24th signing of the season, joining for the remainder of the season with "a conditional obligation to become a permanent deal until the summer of 2024".
The 31-year-old Wood joined Newcastle from Burnley for $US34.5 million ($A49.8 million) one year ago and helped the team avoid relegation. The Magpies are now fourth in the Premier League.
Wood could be available for Saturday's game against Bournemouth if Forest register him by midday Friday.
Wood has scored three goals in 22 appearances this season for Newcastle.
Wolverhampton forward Goncalo Guedes has joined Benfica on loan for the rest of the season — just five months after signing with the Premier League club.
The 26-year-old Portugal international had moved to Molineux from Valencia for $US33 million ($A48 million) but has scored only twice in 18 appearances for Wolves.
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