The Game Of Thrones broadcaster lifted operating profits 12% to £1.6bn in the full year to 30 June, while revenues climbed 7% to £11.9bn over the period.
The financial boost came as full-year revenues leapt above £8bn to £8.3bn in the UK and Ireland for the first time in its history .
Shares were up 6% on the FTSE 100 Index
Group chief executive Jeremy Darroch said the Brexit vote "doesn't really change our thinking on any of our markets."
He added: "Media largely remains a pretty local market and we've got strong presence and on-the-ground operations in each of our markets.
"It certainly doesn't change any view as to the size of the prize ahead of us. The other thing being reflected on is if the UK went into recession.
"As we've seen in the past, when that happens people tend to regress to their homes. They are more careful about where they spend their discretionary income.
"And of course, as you've seen in the last few years, we tend to do well in that environment as we offer a great quality service for families to entertain themselves at home. We are on it. We are very focused as a business. But it doesn't really change our directional thinking."
The company added 445,000 customers in the UK and Ireland for 2016, including 93,000 in the fourth quarter, while total numbers across the group rose by 808,000 to 21.8 million.
Sky said more than six million people watched each episode of the sixth season of Game Of Thrones, while high finance drama Billions, starring Damian Lewis and Paul Giamatti, broke on-demand records with 11 million views.
It added that it was on course to deliver its "biggest year" when it came to driving down costs, as it targeted more than £200m worth of savings on a run rate basis for 201617.
It is also aiming for £400m worth of savings by the end of 2020.
However, the firm said total costs were up 6% across the group for 2016, as it drove more investment into new programming and box sets, but saved money by not renewing Champions League football in the UK and Italy.
Rival BT snapped up the Champions League football coverage from Sky and ITV last year, paying £897m for live coverage over three seasons.
Sky said that churn - the number of people leaving its service - rose to 11.2% in the UK and Ireland for 2016, compared to 9.8% the year before.
Full-year pre-tax profits came in at £752m, down from £1.5bn in 2015.
In Europe, the broadcaster recorded its first operating profit in Germany and Austria, while revenues at its Italian business stepped up 2% to £2.1bn despite operating profit slipping 14% to £50m over the period.
Bridie Barrett, analyst at Edison Investment Research, said the company's overseas operation seems to be "turning a corner", adding that "given a potential UK Brexit slowdown, (this) may well prove very timely - as are the additional £400m of cost savings which will go a long way to offsetting rights inflation".