Blowers, who had a successful five-year stint with Northampton, was to have joined Bristol in time for the start of next season.
But with Bristol number eight Dan Ward-Smith sidelined due to a serious knee injury, Blowers has brought forward his arrival in the west country and will be available for selection against Premiership opponents Wasps on March 4.
Blowers, 31, made his Test debut for New Zealand against South Africa in 1996, and went on to make 11 international appearances.
He moved to England at the start of the 2000/2001 season, proving one of Northampton's most successful signings in the professional era.
Bristol head coach Richard Hill said: "It has been a good season for us so far, but we have a critical few weeks ahead of us.
"We've already lost Wardy (Ward-Smith) for the season, and the win over Newcastle on Sunday came at a price in terms of injuries.
"Andrew was to have joined us for next season, but we have negotiated an early release for him from New Zealand, and given the nature of our season, he is keen to come over and play his part as soon as possible.
"His pedigree speaks for itself. He's in great shape, having prepared for the Super 14 season, and I am really looking forward to him joining us."