Bournemouth’s five-year stay in the English top flight came to an end last weekend despite a 3-1 away win at Everton as the Cherries finished in 18th position.
Howe, who was in his second spell as Bournemouth manager, took charge of the South Coast club in all four of England’s professional divisions.
The 42-year-old led the Vitality stadium outfit to three promotions in six seasons, including their maiden Premier League campaign in the 2015/2016 season.
"Having spent a total of 25 years with the club as both a player and a manager, this decision – made together with the club – is one of the hardest I've ever had to make," Howe, who made in excess of 300 appearances for the Cherries as a player, told fans in an open letter.
"However, although the affection and love I have for this football club will always remain, we collectively feel that now is the right time for the club to go in a new direction.
"Bournemouth will always be in my heart but I firmly believe that now is the right time for the club to have a change.
"I have always ensured that every decision I have ever made as manager has been in the best interests of the club and its supporters, and this is no different."
