Lazaridis, who founded RIM in 1984, will become vice chair of the company's board, while Balsillie will remain a director, but with no operational control.
The board has "unanimously named" chief operating officer Thorsten Heins as RIM's new president and chief executive.
It said that it had acted after its own due diligence, but investors had called for a change after the company lost ground to rivals Apple and Google.
Lazaridis, who was forced to make a humble apology to BlackBerry users last October after an embarrassing global service blackout, recognised that it was time for change.
"There comes a time in the growth of every successful company when the founders recognise the need to pass the baton to new leadership. Jim and I went to the board and told them that we thought that time was now," he said.
"With BlackBerry 7 now out, PlayBook 2.0 shipping in February and BlackBerry 10 expected to ship later this year, the company is entering a new phase, and we felt it was time for a new leader to take it through that phase and beyond. Jim, the board and I all agreed that leader should be Thorsten Heins."
Heins, who joined RIM in 2007 from Siemens and was named chief operating officer in August 2011, said: "Mike created a whole new way of communicating and I look forward to continuing our close collaboration."
He added: "As with any company that has grown as fast as we have, there have been inevitable growing pains. We have learned from those challenges and, I believe, we have and will become a stronger company as a result.
"Going forward, we will continue to focus both on short-term and long-term growth, strategic planning, a customer- and market-based product approach, and flawless execution."
RIM said that Lazaridis will provide "strategic counsel" to Heins, as well as "continue to promote the BlackBerry brand worldwide".
Barbara Stymiest, who has served on the board of RIM since 2007, has been named the new chairman, a post previously shared by Balsillie and Lazaridis.
Lazaridis said that he is so confident in RIM's new leadership that he has confirmed plans to purchase $50m of additional shares on the open market.
"Thorsten has demonstrated throughout his tenure at RIM that he has the right mix of leadership, relevant industry experience and skills to take the company forward," he said.
"We have been impressed with his operational skills at both RIM and Siemens. I am so confident in RIM's future that I intend to purchase an additional $50 million of the company's shares, as permitted, in the open market."
In a statement, Balsillie added: "I agree this is the right time to pass the baton to new leadership, and I have complete confidence in Thorsten, the management team and the company. I remain a significant shareholder and a director and, of course, they will have my full support."
Billions of dollars were wiped off RIM's market value last year as shares tumbled 75% and sales of its smartphones and other products dropped.
The company has massively slashed the price of its PlayBook tablet product after sluggish demand for the tablet and a complete failure to challenge Apple's market-leading iPad.
RIM has also had to delay its new BlackBerry 10 operating system, which will power the company's next-generation smartphones.
However, Heins feels RIM has a "strong foundation on which to build. The firm had around $1.5bn of cash on its balance sheet as of the final quarter of 2011, when it reported revenue of $5.2bn, up 24% of the previous quarter.
"BlackBerry 7 has been well received. We are very excited about PlayBook 2.0 and BlackBerry 10. The reception of our products at this year's Consumer Electronics Show was encouraging," he said.
"RIM earned its reputation by focusing relentlessly on the customer and delivering unique mobile communications solutions. We intend to build on this heritage to expand BlackBerry's leadership position."
He added: "Mike and Jim took a bold step 18 months ago when RIM purchased [operating system] QNX to shepherd the transformation of the BlackBerry platform for the next decade.
"We are more confident than ever that was the right path. It is Mike and Jim's continued unwillingness to sacrifice long-term value for short-term gain which has made RIM the great company that it is today. I share that philosophy and am very excited about the company's future."
> RIM to revive PlayBook with two new tablets in 2012