Arsenal can already boast a small victory over Leicester this week after poaching their Premier League title rival's top scout.
The two sides meet at the Emirates Stadium on Sunday in a crucial clash, with league leaders Leicester currently five points clear of third-placed Arsenal.
"After three-and-a-half unbelievable seasons, working with amazing people, I am now starting a new chapter," Wrigglesworth wrote.
"It was a very difficult decision, leaving Leicester, but I had to take an opportunity that doesn't come round often.
"I only wish the best for Leicester in the future and will always be eternally grateful to them for getting me to where I am."
During his time at Leicester, Wrigglesworth helped to bring in Riyad Mahrez and N'Golo Kante, who have both been vital for the club this season.
Mahrez was signed for just £400,000 from Le Havre in 2014 but has been one of the stars of the Premier League this term with 14 goals and 10 assists.
Kante joined from Caen last summer for a reported fee of around £6 million and has been a key man in the heart of Leicester's midfield.