People had suggested that he breached "generally accepted standards" with his comments, but Ofcom says they won't formally investigate it as the remarks were brief and because regular listeners of Steve's show are used to him being "provocative".
A spokesperson said: "We have provided guidance to LBC to take greater care in future.
"Given societal concerns about body image pressures on young people, the presenter's criticism of a young woman's appearance could have led to an adverse effect on wellbeing and mental health.
"But given the brevity of the comments and the likely audience's expectations of this provocative presenter and programme, we will not be pursuing further."
Tilly had expressed her disgust and sadness to her Instagram followers after being made aware of the comments.
Tilly was on Strictly when Steve called her a "chubby little thing"
She shared the clip, in which Steve was heard saying: "Tilly Ramsay is on Celebrity MasterChef Australia, is she? Well she can't blooming well dance, I'm bored with her already.
"She's a chubby little thing, isn't she? Have you noticed? Probably her dad's cooking I should imagine."
In response, Tilly penned: "I try not to read and listen to comments and negativity however recently being called out on a national radio station by a 67-year-old man is a step too far.
"Steve please feel free voice your opinions however I draw the line at commenting on my appearance. It's such a shame that someone is trying to make such a positive experience negative.
Tilly and dad Gordon
(Image: Copyright unknown)
"This isn't the first and definitely won't be the last comment made about my appearance and I accept that and I'm learning to accept myself.
"But please remember that words can hurt and at the end of the day I am only 19 and I'm so grateful for all the amazing opportunities I have been able to take part in and I understand that being in the public eye obviously comes with it's own repercussions and I've been aware of this from a young age.
"However I won't tolerate people that think its okay to publicly comment and scrutinise anyone's weight and appearance. Love Tilly xx"
Steve later issued a private apology to Tilly.
An insider told the Daily Star: "Tilly has been given a full apology by Steve. He wanted to make it clear that he is very sorry to have upset her. It was sent privately because he didn’t want it to look like it was done for publicity."