The 'Hold It Against Me' singer was confirmed to have accepted her former agent's proposal on Friday (December 16), after which they headed to Las Vegas to celebrate.
However, Alexander, who was married to Spears for 55 hours after the childhood friends wed in Vegas in 2004, has admitted his scepticism over the union and claimed that he can see "no connection" between the couple.
"I know everyone wants me to be happy about this, but I am not," Glamour quotes him as saying. "I think it's fake and I think people are afraid to say it. If you look at all the pictures between them there is no connection.
"They look like they are going through the motions. It seems like an answer to the court thing. Sort of a nice way to sew it all up; she marries her handler. That way she always has someone controlling her. It's sort of sad."
Spears's second husband Kevin Federline this week congratulated the 30-year-old on her engagement, saying: "I'm really happy for her... she's doing really well. I want to say she's in a good place."
The couple were married from 2004 to 2006 and have two sons together, 6-year-old Sean Preston and 5-year-old Jayden James.
Watch Britney Spears in the video for 'Hold It Against Me' below: