The presenter was taken off air after breaking Covid-19 rules with a birthday gathering at the end of last year.
Burley returned to her usual breakfast slot on the news station on Monday morning.
Starting the broadcast at 7am, she said: “Hello everybody, it is great to be back. It is seven o’clock here in the UK. Welcome wherever you’re watching us around the world. Let’s crack on.”
Burley had celebrated her birthday with a rule-breaking gathering in London in December, while the capital was under Tier 2 restrictions.
Burley, who has been with Sky News since its inception in 1989, apologised at the time, tweeting: “It’s clear to me that we are all in the fight against Covid 19 and that we all have a duty to stick firmly by the rules.
“It doesn’t matter that I thought I was Covid-compliant on a recent social event. The fact is I was wrong, I made a big mistake, and I am sorry.”
She continued: “Some dear friends and colleagues – some of the most talented and committed professionals in our business – have been pulled into this episode and I regret this enormously.”
Following an internal review in December, Sky News found that “a small number of Sky News staff attended a social event in London” where Covid-19 guidelines were breached.
It said: “All those involved regret the incident and have apologised. Everyone at Sky News is expected to comply with the rules and the company takes breaches like this very seriously indeed.”