Barrett signed a short-term deal with Leinster in April, and will play the rest of the season in the URC before returning to New Zealand.
The 27-year-old has a connection with Ireland, having spent time in Oldcastle, County Meath when his family lived there in the early 2000s.
The centre also got a special reception from an old Irish rival when he touched down.
"It's great to be here, [I] got the royal treatment, picked up at the airport by [Leinster & Ireland prop] Tadhg Furlong, great to be welcomed by someone like that," Barrett told Leinster TV.
"It's nice to be able to rub shoulders with a lot of boys this week, the internationals are away so I've been seeing plenty of fresh faces in and around the environment and it's a special time that I'm very much looking forward to."
Barrett was in Dublin last month as New Zealand beat Ireland 23-13 at the Aviva Stadium and said it was a unique experience ahead of his move.
"Yeah, it was a special week," Barrett said. "It was one I was looking forward to the minute I signed with Leinster.
"Had it marked in the calendar and it was such a great week. It was different from the times I've been in Dublin before.
"There were plenty of people around Dublin that were happy that I was in Dublin and they kept saying to me 'welcome to Leinster' and that they were glad to have me, so that was pretty special.
"It was a funny feeling playing against a few of the Irish boys who are here with Leinster and knowing that I'll be hopefully chucking on a jersey beside them in a few weeks time, so it's pretty special."
Leinster take on English side Bristol in the Champions Cup on Saturday.