Bill McDermott, SAP's head of field organisation and Jim Hagemann Snabe, head of product development, were named as co-chief executives by the company's executive board, SAP said in a statement released late on Sunday.
Both already serve on the company's executive board, which is being joined by Vishal Sikka, SAP's chief technology officer.
It will be the first time since the company was created in 1972 by five former IBM employees that neither of its two leaders are German.
"The new setup of the SAP Executive Board will allow SAP to better align product innovation with customer needs," said Hasso Plattner, one of the company's founders and chairman of supervisory board.
"The new leadership team will continue to drive forward SAP's strategy and focus on profitable growth, and will deliver its innovations in 2010 to expand SAP's leadership of the business software market."
The company recorded a four-percent fall in net profit last year to €1.8 billion, but expects to bounce back in 2010 with a 30-31 percent jump in operating profit.
To soothe clients who were angered by higher prices for maintenance and computer services, SAP launched in January a basic contract that costs much less than one introduced in 2008.
But the group is still accused of developing more and more complex software without considering how it will be adapted by clients.
Internally, Apotheker was also criticized for a "stiff and direct" management style and for a decision to eliminate 3,000 jobs last year, the first time the group has cut staff.
Analysts welcomed his departure on Monday but wondered about the effect of taking on two product experts, fearing that might raise future costs of research and development.
Merck Finck analyst Theo Kitz also said: "We are concerned that the co-leadership might slow down the decision-taking process."
SAP shares showed a loss of 1.63 percent to €32.84 in midday trading on the Frankfurt stock exchange, while the DAX index of leading stocks was 0.73 percent higher overall.