From the official Web site of the White House, the following is a brief history of the West Wing:

“The history of the West Wing dates to the early years of the White House. President Thomas Jefferson, the first full-term occupant of the White House, proposed one-story extensions to the east and west to connect the President's house with adjacent office buildings. President Jefferson's design concepts survive in part through the terraces that connect the Residence of the White House with the East and West Wings.

“The terraces, as constructed, were used for household functions and did not provide additional office space. The president continued to live and work in the White House proper for the remainder of the century with his executive offices taking up much of the second floor, the same floor as the living quarters. Official and family needs, however, made this arrangement unsatisfactory.

“For example, in 1860 a state visit by Edward, Prince of Wales, distressed the Buchanan administration because of the lack of appropriate guest accommodations. Elaborate schemes were set forth to alleviate the crowded conditions under the Harrison, Cleveland and McKinley administrations, but it was not until 1902, under the direction of President Theodore Roosevelt, that the presidential offices were removed from the Residence to the addition that became known as the West Wing.

“Today, the West Wing is the center of activity at the White House. The West Wing houses the President's Oval Office, the offices of his executive staff, the Cabinet Room, the Roosevelt Room, and the James S. Brady Press Briefing Room.”

Theodore Roosevelt and the West Wing
Also from the White House Web site, the following brief history, plus this page offers a video tour of the facility. Interesting fact: It was President William Howard Taft, who created the Oval Office:

“When President Theodore Roosevelt oversaw the construction of a temporary office building one hundred years ago, he not only permanently transformed the grounds of the White House, but he also transformed the presidency.

“Theodore Roosevelt's temporary office building is known today as the West Wing. His six children and White House staff were crowded on the second floor of the White House. Congress appropriated $65,000 for the construction of a temporary, one-story office building just west of the White House. The White House interior was also restored in 1902.”

Rich and Colorful History
Each President and First Lady brings different qualities to the White House, arising from their own styles and personalities. The history of the Executive branch of government is a rich and colorful one.

Visit the White House Web site for more information:
The West Wing
Life in the West Wing