Bell, 19, made three first-team appearances for Dale in addition to loan spells at Chester and Droylsden.
He follows former Forest Green striker Reece Styche among the Tynesiders forward imports this summer.
"Nyal is a young, athletic striker who is prepared to work hard and willing to learn to go on to the next level," assistant manager Lee Nogan said.

Shiels, whose played for League of Ireland champions Dundalk last year, joins a club that plays in the tier below the MLS in North America.
FC Edmonton are captained by former Linfield defender Albert Watson.
"Dean's a goalscorer and a creative player who works at a level we would expect of someone at FC Edmonton," said Edmonton head coach Colin Miller.
"Dean did very well for my old club Rangers and has had a fantastic career."
The 32-year-old, son of Derry City manager Kenny Shiels, spent four years at Rangers where he played in two promotion-winning teams.
Previously he had spells with Hibernian, Doncaster Rovers and Kilmarnock.
The attacking midfielder from Maghera won the last of his 14 Northern Ireland caps in 2012.
FC Edmonton will begin their NASL season in early April.

Camden Glass, part of the Camden Group, has started a 30-day consultation with staff on the closure of its factory in Benburb, according to Unite.
The firm produces and supplies PVCu window and door products.
Camden Group has told Unite it will be creating 50 new jobs at a new plant in Antrim.
Unite's representative Joanne McWilliams said Camden Group's investment in the Antrim plant was "cold comfort to the workforce in Benburb".
"Many workers in Benburb have longstanding service at the plant - one of our members has worked there for 43 years," she said.
"Many of the workers facing redundancy have built the company's success long before the current management took over.
"To compound [the] decision, management have offered the workforce only the bare minimum, statutory redundancy.
"Camden Group must live up to their social responsibilities and fully compensate their workforce for a decision driven by corporate priorities."

The six-month project at Havelock Europa is expected to "follow the wealth", where market opportunities arise in the UK and globally.
The Kirkcaldy-based firm also wants to extend its sourcing operation in China and grow further in Australia.
The company has already focused its marketing efforts in London.
Office refurbishments in the capital are among Britain's more lucrative opportunities.
The firm has been through a difficult corporate turnaround in recent years.
In announcing its full-year results, the Fife firm said 2016 was "challenging".
Havelock Europa was back into the black, with pre-tax profits of £183,000, following a 2015 loss of £2.7m.
Revenue was down in 2016, largely due to the loss of a major financial client, believed to be Lloyds Banking Group.
Sales fell from £73m in 2015 to £61m.
In trying to diversify its clients away from a few large banks and education refurbishments during academic holidays, the company is seeking to secure more clients from the health sector and student accommodation.
It is also looking for a wider range of retail clients, which have so far included big high street names such as Marks & Spencer, Primark, Accessorize and House of Fraser.
Havelock Europa employs 300 people at its Fife factory and marketing base, with offices also in China and Mansfield in the English Midlands.
The company's shares fell 12% in the hours after the annual results were published.
Gateshead have signed striker Nyal Bell on a two-year deal following his release by Rochdale.
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Northern Ireland strike Dean Shiels has signed for Canadian North American Soccer League club FC Edmonton.
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Sixty-five workers at a County Tyrone manufacturing company are set to lose their jobs, a trade union has said.
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A major Scottish interior fitter has announced "a major review of its longer-term vision, mission and strategy".