The former Wigan Athletic player, 29, has not played since August 2012 due to a cruciate knee ligament injury that has cost him almost two whole seasons.
"What a fantastic feeling it was this morning to be back out training with the team. Moments like that are worth so much to me and my family," Taylor tweeted.
"Thank you so much for all your support throughout my rehab, it's been much easier with the support you guys have given me."
Taylor, who can play at right-back or in midfield, has scored 10 goals in 91 United appearances.