Transport Minister Andrew Stephenson confirmed the cash had been given to Network Rail to remove bottlenecks.
The increased capacity will allow more passenger and freight services including an increase in fast trains to Manchester from two to three an hour.
There will be new sections of track near Bamford to create a loop allowing overtaking, improvement to Jaggers Lane Bridge in Hathersage and a second track at Dore and Totley station which will also have a second platform added.
Construction is expected to begin in 2022 with completion by December 2023.
The news comes as a head of steam is building around Sheffield’s poor rail infrastructure. Only this week MPs united to campaign for four new stations and two new tracks on the congested Sheaf Valley line to the south east of the city.
Reacting to the Hope Valley line news, Peter Kennan, chair of Sheffield Chamber of Commerce Transport Forum, said: “This is such an important scheme for Sheffield and the wait has been nearly 10 years!”
High Peak MP Robert Largan has campaigned on the issue since he was elected in 2019.
He said: “I am absolutely delighted that the Government has listened to the people of High Peak and is moving forward with this £137million investment in the Hope Valley line.
“This is a really big win for the High Peak and the North. This capacity upgrade investment will help deliver a more frequent and more reliable train service.
“This marks the biggest investment in High Peak’s public transport in my lifetime. I want to thank everyone who has supported my campaign. This shows what we can achieve when we all work together!”
Transport Secretary Grant Shapps said it was an example of the Government’s levelling up agenda in action.
Campaigners say Sheffield’s rail network has suffered 40 years of decline, including cancelled services, delayed upgrades and proposed schemes failing to arrive at all.
Today, it is the largest city and busiest station not on the electrified network, its position on the HS2 route is uncertain and the main benefits of Northern Powerhouse Rail are further away still.
David Hoggarth, strategic rail director at Transport for the North, said they had repeatedly made the case for the project on behalf of the region’s civic and business leaders.
He added: “This line has suffered for years with slower trains holding up faster ones, leading to cancellations, delays and unreliable services for passengers. It currently has some of the slowest train speeds on the North’s rail network, meaning people often resort to travelling by car.
"It’s great news that investment will now go into this vital commuter corridor, whilst longer-term upgrades as part of Northern Powerhouse Rail are finalised.”
Transport for the North’s latest statutory advice to Government also calls for longer-term, significant investment in the Hope Valley corridor as part of the Northern Powerhouse Rail network. This would eventually speed up journey times and increase frequency.
Northern Powerhouse Rail is expected to feature in the Government’s Integrated Rail Plan, anticipated to publish shortly.