The 24-year-old joins the Scottish Premiership champions from Qarabag, where he netted 15 goals and provided 10 assists, per the Official Celtic FC Website.
Duran will now continue his career in Glasgow under boss Martin O'Neill and will travel to meet his new teammates at their pre-season training camp in Portugal.
Speaking after signing for the Hoops, Duran said: “I'm very happy, it's a dream come true to sign for a big club like Celtic, the biggest in Scotland, and I'm just excited to get going and score lots of goals.
“When I first heard of the interest there was absolutely no doubt in my mind and I'm just excited to get playing with the boys.
“It's an honour to be the first Colombian to play for Celtic. It's been a dream of mine since I was a kid (to play for my country) and I hope that being here at Celtic and working well, then one day that will become true."