The Scottish football legend died at the age of 73 prompting tributes from far and wide.
Smith, synonymous with Rangers, spent a large part of his career at Tannadice, fulfilling a number of different roles, including player, assistant manager, and board member.
United, in a statement, said they were "deeply saddened to hear of the passing” of their former star.
It read “Originally signed from Junior side Ashton in 1966, Walter was part of the 16-man squad that travelled to the USA after United were invited to play as Dallas Tornado in the United Soccer Association. He became a regular in the team in 1971 and played in our first Scottish Cup final in 1974 before leaving to join Dumbarton in 1975.
“Returning 18 months later, Walter suffered a career threatening injury and was elevated to a player/coach role by Jim McLean. Smith was first team coach as United entered the most successful period of their history so far, winning two League Cups and the Premier Division title in the early 1980s. He went on to become the national Under-21 coach and then assistant manager to both Jim McLean at United and to Alex Ferguson in the Scotland set-up and was elevated to the Tannadice board in February 1986.
“In 1986 he left to join Rangers as assistant to Graeme Souness, becoming manager in 1991 and enjoying several successful years at Ibrox before continuing a hugely successful managerial career that saw him managing Everton and Scotland before returning to Ibrox before retiring in 2011.
"Dundee United extends its condolences to Walter's extended family at this difficult time.”