Mather had been serving as executive vice president of finance and ballpark operations. He has been with the team since July 1996 and had held that position since 1999. Mather oversaw Seattle's financial and ticket services, retail operations, technology and daily operations of Safeco Field, among other duties.
Armstrong, 71, had been Seattle's team president for 28 of the previous 30 seasons. Armstrong announced he was retiring in late November citing a desire to spend more time around friends and family.
"His experience in the game of baseball has prepared him well for this position," Mariners Chairman Howard Lincoln said. "He is highly thought of around Major League Baseball and in this community. He will work closely with me to make sure Jack Zduriencik has the resources he needs to build winning teams. Jack remains the leader of the baseball side of our organization."
The 51-year-old Mather worked for the Minnesota Twins before joining the Mariners. He is a native of Madison, Wis., and a 1984 graduate of the University of Wisconsin.
"Our fans, first and foremost, are our focus, and we understand what they want most - a championship team," Mather said in a statement. "I am looking forward to supporting Jack Zduriencik, as he continues to lead the baseball operation and builds the Mariners both for 2014 and for future seasons. At the same time, our commitment to this community and this region will remain a top priority. This is a tremendous opportunity, and I'm excited about the Mariners future."
Seattle also announced the promotion of Bob Aylward to chairman of NW Sports Net LLC. That is the entity that oversees operations of ROOT Sports, the regional sports network the Mariners own a majority stake in. Aylward will retain his position as the executive vice president for business operations for the team.
Aylward, 60, joined the club in 1997 and oversaw all business aspects as the team moved from the Kingdome to Safeco Field. He was promoted to his current position in December 1999.