The broadcaster told RadarOnline: "We are thrilled for them. We love Amal. We think they’re a wonderful match and wish them well."
Nick Clooney says Amal and his son are "a wonderful match"
Speaking to US Weekly, he added: "We are thrilled. We have had an opportunity to interact with this wonderful young woman and these are two great people."
His feelings were echoed by George's mum Nina, who confirmed the couple's engagement on Monday.
The 74-year-old said: "I like her very much," adding: ""You can say I'm extremely happy, Amal's a lovely girl.
We weren’t at all surprised when they told us they were engaged, and we couldn’t be happier for them. On an intellectual level, they are equals. That is very important to him. Amal’s world couldn’t be more different from the Hollywood lifestyle."
The couple are thought to have only been dating a few months
When asked by MailOnline if Amal was very similar to the other girls George has dated, she replied resoundingly with: "Heavens, no! She’s a lawyer, she is brilliant, she is a very bright woman and at the very top of her career. They also share a sense of fun, a sense of humour and they are both very caring people."
The general consensus among the family is that Amal is a very special girl indeed to have taken eternal Hollywood bachelor George off the market.
His aunt Starla Clooney said: "I’m just as surprised as the rest of the world. George was going to be a bachelor his whole life.
Amal in 2012 at a press conference in support of imprisoned former Ukrainian leader Yulia Tymoshenko
"This woman must be exceptionally special to him for him to take the plunge. He hasn't seen her very long. In the past there has at least been some sort of length of time."
Lebanon-born Amal is an adviser to former UN Secretary general Kofi Annan and is also the special envoy to Syria, and she reportedly played hard to get by using her strategic planning skills.
A source revealed that George apparently asked her out for dinner and she told him twice that she was too busy before accepting the third time.
"She was operating on the lines of "treat ‘em mean, keep 'em keen" and clearly it worked," said a source.