Reeves was photographed holding hands with artist Grant as they attended an event here on Saturday, reports dailymail.co.uk.
At the event, the actor, 55, and the artist, 46, didn't let go of each other, and exchanged loving glances while posing for photographs in front of the press. He beamed at her and held her hand as he walked past photographers and the press while heading into the museum.
Reeves looked smart in an all-black suit, while Grant looked graceful in a navy blue gown, heels and bangle bracelets. Reeves has collaborated with Grant on the books "Ode To Happiness" and "Shadows". The business partners also have publishing house X Artists' Books.
For weeks there have been rumours, Reeves has gotten serious with the artist.
The couple looked very happy in mid October when they were arm in arm as they left a sushi bar on Sunset Boulevard in Los Angeles. Grant was seen resting her head on Reeves' shoulder as they strolled.
Reeves has always keep his personal life very private. He has been linked to Amanda De Cadenet, Sandra Bullock and Claire Forlani in the past.
For much of the 1990s, he was with Jennifer Syme. They faced heartache in 1999 when their daughter Ava was born stillborn at eight months.
In 2001, Syme drove her car into a row of parked cars in Los Angeles. She died instantly. She was 28-years-old at the time of her death.
( With inputs from IANS )