Nazmul Hassan said that the Afghan team, who are based in India, had agreed to play three ODIs at Dhaka's Sher-e-Bangla National Stadium on September 25, 28 and 30.
"Our senior players recommended the series. So we invited Afghanistan to play against us," Hassan told reporters late Sunday.
The matches will be the first ODIs hosted by Bangladesh since last year when they won series against Pakistan, India, South Africa and Zimbabwe.
England are due to arrive in Bangladesh on September 30 for three ODIs and two Test matches despite concerns over security.