Claire Williams wanted a "fresh" and "bright" new livery to mark an end to the British team's horror period.
Williams, a once-great name in F1, finished dead last in 2018 and lost the backing of title sponsor Martini.
The team has a new sponsor for 2019, and Claire Williams said that was the perfect opportunity for a new livery.
"Frank loved it, and you might be surprised to hear that," she said as the new mainly white and sky blue livery was unveiled.
"I was a little nervous presenting it to him but he is fully behind it. If he didn't like it, he would have fired me," Williams, team founder Sir Frank's daughter, added.
Williams said the new look is "fresh" and "bright", and hopes the performance will get a major lift in 2019 as well.
"Last season was very difficult, but over the winter almost nobody left, which speaks of the strength of spirit here at Williams," said Claire.
"What was happening could have destroyed the team. We could have gotten bogged down in an internal struggle or dismissed half of the staff, but we didn't want to do that.
"We know our weaknesses. You don't go from fifth to tenth in the championship without a good reason. We have done a lot of work, but the way back up will take time," she added.
