Police Scotland staff are operating "inefficiently" with either no or out-of-date mobile phones.
The Scottish Police Authority (SPA) was also told there is an "urgent need" for modern devices.
A report to the SPA's public board meeting estimates the new phones and the necessary support network would cost £21.6m.
It is forecast the investment would generate around £49m of efficiency savings over a five-year period.
The force's Deputy Chief Officer David Page said this would be the equivalent of 400 extra officers.
Meanwhile, the related national network infrastructure could deliver savings of £7.5m over seven years.
Mr Page said the investment is "absolutely critical" for officers who would be spared having to enter data multiple times or returning to base to get more information.
He said: "Our communities will see our officers in their space much more frequently, our officers won't be travelling back to their bases, will be given better information to do their job.
"It's a huge enabler for officers to become much more productive and much more visible in their communities.
"The investment in the national network is what we need to do to stop our systems from creaking and going out of date, but also to allow them to support mobility."
Mr Page told the board the initial plan is for the roll-out of 600 devices by the end of the financial year, with the full 10,000 to follow.
Elaine Wilkinson, who chairs the SPA finance committee, said the business case has the support of the board, but added: "We don't take investments of this level lightly without looking at the benefits.
"We need to ensure that we don't just understand how much we're spending but the reality of the returns that we're getting on that."
The board also heard a defence of a new strategy for greater collaboration between Scotland's emergency services.
The document sets out proposals including the development of a joint dementia strategy, the embedding of specialist mental health staff in control rooms and the possibility for each of the services to feed into the training of new recruits.
The Scottish Police Federation (SPF) had raised concerns that officers were already struggling to cover their work without taking on further duties.
Responding to the comments, SPA chair Susan Deacon said: "Some have expressed concerns in the press today that collaboration might mean a diminution of people's specialist capabilities.
"I don't think anything could be further from the truth.
"The most effective collaboration is that which recognises the specialist skills that different people and organisations have and finds ways of how they can work better together.
"There's no question in my mind it has to be the way forward for public services in general in Scotland as well as policing in Scotland.
"I'm very pleased that that work is ongoing."
The proposed merger between the force and British Transport Police was also discussed at the meeting in Glasgow.
Chief Constable Iain Livingstone reiterated that force's position that it is not yet in a position to recommend a revised 'go-live' date to the SPA.