Smith was expected to miss the entire season-ending northern hemisphere tour to stay home with family after the birth of his second son Leo but could line up in the final two tests against the Irish and France.
"It all happened very quickly and now I'm two hours from jumping on the plane to join the boys in Ireland," Smith said in a video posted on the All Blacks' social media account on Tuesday.
"I've very excited to come back and join the boys ... Two very big games for the lads, which is really exciting to be part of.
"I'm just looking to try and help where I can, and bring a bit of energy."
The All Blacks face Ireland on Sunday after setting world records for the most test points and tries in a calendar year from their 47-9 win over Italy over the weekend.
Weber was injured early in the match in Rome.
Smith said his wife Teagan was all for him rejoining the side.
"It was a pretty short conversation. She was like, 'Go, this is a great opportunity for you.'
"I'm going over with no expectations of playing, but I'll try to do my best to impact where I can."
The All Blacks will also be boosted by the availability of stalwart lock Brodie Retallick, who has recovered from a shoulder injury sustained in the win over Wales last month.