The $5 million project is funded through the Government's shovel ready Crown Infrastructure Partners (CIP) programme, which Jones secured during his tenure as Minister for Regional and Economic Development.
He said he was pleased for the community to see the project nearing completion.
"I think the community will thoroughly appreciate the quality of this infrastructure, it will improve our harbour and will hopefully improve access for locals to either swim, catch fish or just stop and contemplate the beauty of their home," Jones said.
"I'm happy the local whānau have joined with the community and we acknowledge this important piece of infrastructure.
"It's been an awkward journey with a few cultural bumps in the road, however, the most important thing is that no one is dissenting in relation to improving the infrastructure of the North."
The culvert has been in the spotlight in recent months over a dispute between some local hapū members over the correct name of the area in which the culvert lies.
Matarahurahu hapū kaumātua Freddie Matthews has been steadfast in his belief the correct name for the area is Tokatoka, not Papakawau - the culvert project's original name.
Following a hui at Kenana Marae on Saturday to discuss the name, Matthews said he was pleased with the final result and was looking forward to seeing an improvement in the environment.
"I was concerned about the name and also about getting the environment right and hopefully back to being like it was before this causeway came in," Matthews said.
"Once upon a time we had a very unique ecological system here."
Waka Kotahi NZTA Tāmaki Makaurau me Te Tai Tokerau maintenance and operations manager Jacqui Hori-Hoult said it was rewarding for all those involved in the journey and to witness fish swimming and jumping through the estuary on the morning of the blessing.
"This speaks to the very heart of the project, which aims to restore the marine environment and provide suitable habitat for fish and infauna in the Aputerewa Creek's upper estuary," Hori-Hoult said.
"Waka Kotahi is respectfully awaiting the outcome of hapū discussions with regards to the name."
According to Waka Kotahi, the final stages of works at the culvert were on track and due to be complete by April.
