Lenovo Group Ltd. Is setting an ambitious goal of becoming the world’s largest computer-server maker, as it expects to complete its $2.1 billion acquisition of International Business Machines Corp.’s IBM -0.22% low-end server business this week.lenovo

“We want to win more market share from competitors,” Lenovo Chief Executive Yang Yuanqing said in an interview. “We will not be satisfied.”

Lenovo, which bought IBM’s personal-computer business in 2005, is already the world’s largest PC maker after overtaking U.S. rivals Hewlett-PackardCo. HPQ -1.13% and Dell Inc. Now, Lenovo is taking on H-P and Dell in the server market, with the acquisition of IBM’s x86 server unit. The deal turns Lenovo, still a relatively minor player globally, into one of the major players in the roughly $50 billion server market.

The company said Monday it had gained all the necessary approvals for its IBM server acquisition and that the deal is expected to close Wednesday.

Lenovo’s expansion in the server market is also an attempt to find new engines for growth beyond the saturated PC market. While the company generates about 80% of its revenue from desktop and laptop PCs, it is trying to expand to other businesses such as servers and smartphones. Apart from the IBM server acquisition, Lenovo is in the process of completing another deal to buy the Motorola Mobility handset businessfrom Google Inc. for $2.91 billion. The Motorola deal hasn’t closed yet.

“We have a lot of work to do internally,” Mr. Yang said.

As soon as it completes the acquisition, Lenovo plans to start integrating IBM’s workforce. Adalio Sanchez, an IBM executive who heads the x86 server unit, will continue to lead the business after the acquisition, Lenovo said in a statement Monday.

Since Lenovo announced its plans to buy the IBM server unit in January, concerns among IBM customers about the transition have created opportunities for competitors to take market share from IBM.

Mr. Yang said that the deal’s closure will help ease concerns among customers. “No matter how much share competitors have gained from IBM, we will get it back,” he said.

Mr. Yang added that IBM’s x86 server unit is already a profitable business, and Lenovo will try to make it more profitable.

“IBM has very good technology and very strong engineers….but the industry is changing,” Mr. Yang said. As IBM’s current cost structure makes it difficult to compete in the fast-changing market, Lenovo will work on making the business more efficient, he said, without disclosing specific restructuring plans.

Mr. Yang said Lenovo expects higher profit margins from servers than those from PCs. In the first year after the acquisition, Lenovo expects combined revenue of $5 billion from its own server business and that formerly of IBM. Lenovo executives declined to provide the current combined revenue figure, but said $5 billion in revenue would represent substantial growth. Lenovo’s 2013 revenue was $38.7 billion.

Executive Vice President Gerry Smith, who oversees Lenovo’s businesses for corporate clients, said it was still too early to discuss whether Lenovo would reduce the IBM unit’s workforce after the acquisition.

Messrs. Yang and Smith, in their combined interview, said the company’s long-term goal is to become the No. 1 player in the server market. Mr. Smith said Lenovo aims to achieve that goal in five to seven years, following on its ascent in the PC market.

“Our competitors had better be wary because we are coming at them and coming at them hard,” Mr. Smith said.

Lenovo said the IBM server deal has come in at a lower value than the previously announced $2.3 billion in part because of a change in the valuation of the IBM unit’s inventories, but the deal’s terms haven’t changed.

In August, Lenovo said its proposed acquisition of the IBM unit passed the U.S. government panel that screens deals with possible national-security implications.