Wright, who has been chief executive of Age UK for eight years, will join Guide Dogs in September, replacing Richard Leaman, who left the charity at the end of November.
Wright joined Age UK in January 2009 to oversee its creation through the merger of Age Concern and Help the Aged.
The merger was not without its difficulties, with some independent Age Concern charities refusing to join the new brand.
Before joining Age UK, Wright was chief executive of VisitBritain, which markets Britain as a tourist destination. Prior to that, he was managing director of Saga Holidays.
A spokeswoman for Guide Dogs said the charity would not release details of Wright’s salary until its accounts for 2017 were published, which is not likely to be until at least July 2018.
Guide Dogs’ most recent accounts show that Leaman was paid £146,013 in the year to 31 December 2015.
According to its accounts for the year to 31 March 2016, the highest-paid person at Age UK, who is not named, received between £190,001 and £200,000 a year.
On his appointment at Guide Dogs, Wright said in a statement: "It is an exciting time to be joining the charity because it is doing more now than ever before to help people who are blind or partially sighted gain freedom and independence."
Jamie Hambro, chair of Guide Dogs, said Wright would bring a "wealth of experience" to the charity.
"He has the knowledge, experience and background to lead the organisation and ensure the delivery of a range of life-changing services to those living with sight loss," said Hambro.
Dianne Jeffrey, chair of Age UK, said her charity would be sorry to see Wright go.
"He's spent nine years as our chief executive, so we appreciate his desire for a fresh challenge leading another well-known national charity, and I wish Tom every success for the future," she said.
Guide Dogs said Steve Vaid, its acting chief executive and director of mobility services, would be promoted to chief operating officer.
Steph Harland, deputy chief executive of Age UK, will become acting chief executive while a new chief executive is sought.