The 27-year-old, who has won 22 caps and featured at the 2011 World Cup, joined the Exiles on a short-term deal in November, with a view to him remaining for a further two seasons.
And the Exiles have chosen to take up that option after Treviranus made a strong initial impression upon his arrival at the Madejski Stadium.
He then returned to his homeland for the birth of his son, but came on as a replacement in Sunday's Aviva Premiership defeat to Leicester.
"I have really been enjoying my rugby and my time at the club so far," he said.
"I like the style of play and feel that I am making fantastic strides in my development as a player. It's great to be back."
London Irish head coach, Toby Booth added: "I have been impressed with the way Ofisa has fitted into the squad and with his performances.
"He brings a hugely physical approach every time he takes the field and is a natural ball winner on the floor."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.