Dinnage joins from media organisation Discovery, where she was the global president of the Animal Planet channel.
Scudamore, 59, is stepping down next month after 19 years at the helm.
“I am excited at the prospect of taking on this fantastic role. The Premier League means so much to so many people,” said Dinnage, who will begin her new job early in 2019.
“It represents the pinnacle of professional sport and the opportunity to lead such a dynamic and inspirational organisation is a great privilege.
“With the support of clubs and the team, I look forward to extending the success of the league for many years to come.”
Dinnage will become just the third person to lead the Premier League, after Scudamore and his predecessor Rick Parry.
Prior to joining Discovery in January 2009, Dinnage worked for 10 years at Channel Five and she started her career at MTV.
“We are very pleased to appoint such a capable leader to this important role,” said Bruce Buck, Chelsea’s chairman and chair of the Premier League’s nominations committee.
“We had a very strong field, but Susanna was the outstanding choice given her track record in managing complex businesses through transformation and digital disruption.
“She is a leading figure in the broadcasting industry, a proven business executive and a great developer of people. She is ideally suited to the role and we are confident she will be able to take the Premier League on to new heights.
“Richard Scudamore, having provided exceptional stewardship for almost 20 years, will leave us at the end of the year in great shape and with an excellent executive team and board able to fully support Susanna.”
Scudamore was the Premier League’s executive chairman but the top-flight clubs had already agreed to split his role. The search for a non-executive chair will now begin, the league said.