The TV presenter met roofer Cockings, 26, on Twitter and the pair exchanged explicit tweets with one another at the start of their fling.
"To my beautiful twitter friends just want to let you know that me &Jack @bespokespartan are engaged to be married and we are very giddy xxxx," Sykes confirmed on Twitter.
Cockings proposed to Sykes on her 42nd birthday last week, The Sun reports.
She was seen wearing an engagement ring on ITV1's Let's Do Lunch with Mel and Gino.
"Jack the rabbit I need some bunny love so hop to it!! xxxxxxx," was one of the messages from Sykes to Cockings as they started dating.
Cockings replied: "Only if I can bounce into your face."
Sykes later defended their exchanges, saying: "I like my men wild and unscripted. I'm so naughty, what can I say? I'm a cheeky gal."
Cockings maintained earlier this year that he was not dating chef Heidi Caswell when he was sleeping with Sykes.
He was hospitalised earlier this month with a snake bite and posted a picture of his injury on August 7 - the day he is reported to have proposed to Sykes.