The midfielder will be teaming up with another former Trotters player Christian Doidge.
Hibs have announced the signing of the former Wanderer.
The 25-year-old midfielder spent 17 years with Bolton, making more than 180 appearances for the Lancashire club. He was a free agent after his contract expired at the end of June.
Hibs head coach Paul Heckingbottom said he was "delighted" to have signed Vela, adding: “Josh will add energy and a competitive edge to our midfield.
“He is an all-round midfielder with the athleticism to support attacks and play on the front foot, helping us win the ball back.
“He was worth the wait and I’m glad we were patient in order to land him.”
Vela added: "Hibs were persistent when I had offers from other teams and that played a big part in me coming here.
“Every player wants to feel wanted and I was really impressed with everything that I heard, then what I saw when I came for a look myself.