Browning has played five Premier League matches already this season, with Seamus Coleman currently out injured.
And Unsworth, who has coached the full-back at under-21 level, says that he is not surprised to see him shining in the senior squad.
“In my opinion, he has been ready for a while,” Unsworth said. “He’s had to be patient and has shown a fantastic attitude to keep working. Whenever he has got that opportunity, he has had to be ready when called upon. He's certainly taken it and I am very proud of him.
“It’s just the start of his career and it’s been great to see him in these big games. What people don’t see is the work he has done behind the scenes and the dedication to our club.”
Browning's form has helped Everton put together a very impressive start to the campaign, where they have moved into seventh place in the table.
The 19-year-old has been part of a backline which has conceded just five goals in the games that he has played, but it is unlikely that he will keep his place once Coleman returns.
The Republic of Ireland international is expected be fit again after the international break, and it could be that Browning has to return to the youth-team at that point.
Everton's next game comes against Manchester United, where Browning will hope to continue to impress, if given another opportunity.