The couple have been together only six weeks.
"Time doesn't matter to me. It could be two days or two years, it doesn't matter," he said.
Morrison said the couple began their relationship through Twitter and talked until he decided to ask her out.
"We have mutual friends but we got talking on Twitter and she must have liked me from that. Then we went out one night and that was it," he said.
The couple celebrated the engagement with friends at a party at Morrison's Kingsland home on Thursday night.
The pair were spotted shopping in an upmarket boutique in Newmarket on Friday and attended an adidas party later that evening. It was there that a couple of people in the group they were in were warned for liquor ban breaches, police confirmed.
Castle-Hughes' spokeswoman Phoebe Miller said the couple were planning a summer wedding.
"They are not going to wait too long, possibly summer. It's been a big surprise for her and she's still telling family and celebrating. She's definitely very happy and very excited," she said.
Morrison, who tweets under the name GetBan, has a show on Base FM and plays as part of DJ group Texas Toast. He also owns a screen printing company.
Last year, he featured in an online video that poked fun at drink-driving which was condemned by police.
The Whale Rider actress has spoken publicly about her battle with alcohol in the past and was spotted leaving an Alcoholics Anonymous meeting in late 2009. She told a women's magazine in 2010 that giving up alcohol was one of the most positive things she had done in her life.
However, the actress and her new partner have posted pictures of parties and alcohol.
One picture the star tweeted featured plants which appeared to be cannabis and last Sunday she tweeted: "Cocaine off the coffee table before the children finish school merits being a desperate housewife, right?"
Her agent Gail Cowan said Castle-Hughes was "mischievous".
"She knows media follows her Twitter so I wouldn't take what's on there too seriously," she said.
The engagement comes soon after a split with her former partner Michael Graves.
He was charged with assault after allegedly grabbing Castle-Hughes during an argument in his car in February, however police dropped the charges.
In March last year, Castle-Hughes was taken away in handcuffs from a central Auckland nightclub following a fight. Graves reportedly came to the defence of his girlfriend when another patron made a derogatory remark about her.
Castle-Hughes and Graves were also involved in a dispute over alleged damage to their $1.4 million Mt Eden rental home.
In 2010, Castle-Hughes split with Bradley Hull. They have a daughter Felicity-Amore, who lives with Hull.