The painter was present for the "cutting off" ceremony at the Dovecot studios, Edinburgh, where the tapestry has been made for the last nine months.
The tapestry, worked on by up to four weavers at any one time, is 18ft 4in by 13ft 9in and will decorate the new foyer of the Theatre Royal, Glasgow.
Entitled Butterfly, it has been designed by Ms Watt, with the weaving led by Dovecot's Master Weaver, Naomi Robertson.
The work will be installed in the theatre's new foyer this summer, hanging over three floors.
In keeping with tradition the weavers did not cut the tapestry from the loom themselves - the threads were cut by Ms Watt, as well as the chairman of Dovecot, Alastair Salvesen; its director, Elizabeth Salvesen; Ian Robertson, Theatre Royal chairman; and Colin McClatchie, Scottish Opera chairman.
The inspiration for the tapestry is opera, in particular the story of Cio-Cio San, the central character to Puccini's opera Madama Butterfly.
The design by Ms Watt references Oriental art as well as the obi, the sash worn as part of the Japanese kimono.
Ms Watt worked with Naomi Robertson and Dovecot to create the tapestry based on her design.
This process began in January 2013, with weaving beginning in August last year.
Ms Watt said: "I was very aware of Madama Butterfly playing an important role in the history of Scottish Opera. It was the first opera its founder Sir Alexander Gibson conducted for Scottish Opera and also his last.
"I wanted to create a piece that echoed the great drama and atmosphere experienced through live performance and from the beginning Madama Butterfly has always been my inspiration."
Ms Robertson added: "It is always extremely exciting to create a new piece of work in collaboration with an artist.
"The sampling process, where we worked together in intensifying the colour choices, took us a number of months and it was a creative challenge to find the most suitable technique for the weaving itself that could achieve seamless gradation of colour."
David Weir, director of Dovecot Studios, said the work was "Dovecot tapestry at its best, drawing together many rich ingredients ... a powerful and dramatic tapestry, full of subtle gradations of colour and texture."
Alex Reedijk, general director of Scottish Opera, said: "This beautiful tapestry is the perfect bridge between the 21st century natural materials of the new foyers and the 19th century lush, gilded interior of the auditorium."
On cutting the tapestry from the loom, Ms Watt said: "It was a very nervous and emotional moment, because I have never unveiled something that I haven't seen before.
"I suddenly felt very attached to the work. When I was cutting it they said 'there's no going back now' and I felt that."
Scottish Opera soprano Catrin Aur, currently in the company's production of Madama Butterfly, sang at the ceremony.