Maeda was part of Japan's squad at this summer's World Cup, helping his country reach the last 32 before they were eliminated by Brazil.
He leaves Celtic as one of the club's most decorated modern-era signings, having scored 79 goals in 212 appearances since joining and won five league titles, three Scottish Cups and two League Cups during his time at Parkhead.
"I have always dreamed of playing in the Premier League and I am very happy I can realise that dream with this club," Maeda told Ipswich Town's official website. "I have loved all of the conversations with the club and they have made me feel very welcome.
"My aim will always be to battle hard, score goals, and provide assists for my team - I will always run and give everything that I have."
Ipswich manager Gary O'Neil, who replaced Kieran McKenna at Portman Road this summer after the club finished second in the Championship to secure an immediate return to the Premier League, said he expects Maeda to make an instant impact.
"He works extremely hard and has impressive physical attributes, while also proving over a number of years playing in Scotland that he has the ability to score goals and create for his team," O'Neil said, with the forward expected to provide competition and cover across the front line as Ipswich prepare for life back in the top flight.
Maeda becomes Ipswich's fifth outfield addition of the summer, following the arrivals of defender Issa Diop, winger Abdul Fatawu, striker Emersonn and goalkeeper Kayne van Oevelen, while defender Cedric Kipre and forward Chuba Akpom have also signed permanently after impressing on loan last season.
The Japan international marked his exit from Celtic with a lengthy tribute to supporters on social media.
"The last four and a half years at Celtic have been the most special chapter of my career and my life," he wrote. "It has been an incredible honour to wear this badge, to play for this amazing club, and to share so many unforgettable moments with my teammates, the staff, and the best supporters in the world. Thank you for standing by me through every high and low."