Derby's new owners believe they can ultimately turn the club into one which will thrive in the Premier League.
Jewell and Appleby will look to turn around Derby's fortunes
The American-based group General Sports and Entertainment (GSE) has agreed an investment partnership which will not involve them taking on any debt.
GSE chairman Andy Appleby said: "If we can build on its strong foundations, there's no reason why Derby cannot be a perennial Premier League club.
"We are excited about this opportunity and impressed by the club's potential."
Derby manager Paul Jewell claimed he was "very comfortable" with the new set-up.
"One of the reasons I came here (in November) was this deal hopefully happening," he said.
"This club has come a long way in a short space of time, and if we build from the bottom up correctly we're hoping it will become great again.
"The people who have come in have the same ambition and excitement as I have to build Derby into a top 10 Premier League team."
Adam Pearson, who retains his position as chairman, confirmed the £50m figure quoted in reports about GSE's takeover was broadly correct.
He said: "It's a great deal for the club, a big figure in the current (financial) climate, and we're delighted to have secured it. We are now very securely funded for the future."
Appleby joins Pearson on the board, while Tom Glick, an ex-chief marketing officer for the New Jersey Nets NBA team, is to be president and chief executive. Another GSE affiliate, Tim Hinchey, becomes executive vice-president.
Derby are the fourth Premier League club in American hands, along with Manchester United, Liverpool and Aston Villa.
BBC sports editor Mihir Bose believes the deal represents good business for the Americans, while also benefiting Derby who will receive "around £10m for players".
He said: "Given that the investors are paying £20m for the shares of Derby, this for them is a very good bargain in a franchise which they can see making them money.
We're talking about cash injection, not debt injection
Derby chairman Adam Pearson
"Yes the fans may hope that the team will benefit and the talk is that the investors will invest in players. But they will also want to develop Derby as a brand."
The Rams have endured a torrid ride since returning to the top flight as they have won just one of their 23 league games this season.
They were also knocked out of the FA Cup by Championship Preston on Saturday.
Speaking in Derby's match day programme on Saturday, Pearson said: "The long-term aim is to establish the Derby brand worldwide through successful alliances with sporting teams in the USA, Far East and other continents.
"The immediate aim is to continue to build the infrastructure of the club at Pride Park and develop a squad which, over the coming seasons, is renowned as a Premier League force.
"The turnaround in the fortunes of Aston Villa, with their American investment in squad and club infrastructure, is a key model we would like to emulate."