Visser has been selected alongside Edinburgh team-mate Tom Brown, who plays full-back, and three Glasgow Warriors, prop Ryan Grant, back-row/lock Robert Harley and lock Tom Ryder.
Injuries and suspensions have hit the Scotland squad ahead of the Tests with Australia (June 5), Fiji (June 16) and Samoa (June 23) and the cancellation of the non-Test fixture with New South Wales Waratahs meant the squad was scaled back to a 28-man group.
Hooker Ross Ford has retained the captaincy after being skipper during the Six Nations, while Ruaridh Jackson has missed out on selection in favour of Warriors team-mate Duncan Weir.
Visser was the PRO12 Players' Player of the Year and leading try-scorer, making a vital contribution as Edinburgh reached the Heineken Cup semi-finals.
He will on June 12 be eligible for Scotland, qualifying on the grounds of three years' residency following his move to Edinburgh from Newcastle Falcons.
Visser, who will be 25 on May 29 and has scored 43 tries in 74 appearances, will therefore miss the opening Test with Australia on June 5 in Newcastle.
After the cancellation of the only non-Test fixture, he may first pull on the dark blue jersey in Fiji.
Visser told Scottish Rugby's website: "I'm very honoured, having lived here for such a long time now I've got to know the country and the people very well and I feel very much part of the country.
"I feel really at home here and the people have been great. I would love to represent Scotland."
Visser's commitment is a welcome boost for a Scotland side who have struggled to score tries and are seeking to arrest the worst run since 1998 after seven successive losses.
Scotland head coach Andy Robinson said: "This is a tough tour for Scotland.
"We'll be playing against three attack-minded teams on their own turf.
"But it's an important opportunity to start the rebuilding process after a disappointing Six Nations."
The core of the squad comes from the group which finished with the Six Nations wooden spoon after defeat to Italy in March, but Edinburgh prop Allan Jacobsen has been rested, joining injured number eight David Denton (ankle) and wing Lee Jones (shoulder), plus suspended lock Jim Hamilton, in missing the tour.
Flanker Kelly Brown (leg) missed the Six Nations and remains absent.
Weir, who led Glasgow to the PRO12 play-offs, Edinburgh centre Matt Scott and Warriors prop Jon Welsh are included after making their maiden Scotland appearances during the Six Nations.
Robinson added: "One quarter of the squad has yet to start an international but we've seen from the manner in which Edinburgh and Glasgow have finished the domestic season that there's confidence that we will be looking to build on."
Robinson will be joined on tour by assistant coach Scott Johnson, but Matt Taylor, who has agreed to join as defence coach, will continue his duties with Super Rugby Queensland Reds and is not part of Scotland's touring party.
Johnson and Taylor replace Gregor Townsend and Graham Steadman, whose contracts were not renewed after the Six Nations.
Backs: J Ansbro (London Irish), M Blair, T Brown (both Edinburgh), C Cusiter (Glasgow Warriors), N De Luca (Edinburgh), M Evans (Castres), A Grove (Worcester Warriors), S Hogg (Glasgow Warriors), G Laidlaw (Edinburgh), S Lamont (Scarlets), M Scott (Edinburgh), T Visser (Edinburgh) and D Weir (Glasgow Warriors)
Forwards: J Barclay (Glasgow Warriors), G Cross, R Ford (capt) (both Edinburgh), R Grant, R Gray, D Hall, R Harley, A Kellock (all Glasgow Warriors), S Lawson (Gloucester), E Murray (Newcastle Falcons), R Rennie (Edinburgh), T Ryder (Glasgow Warriors), A Strokosch (Gloucester), R Vernon (Sale Sharks) and J Welsh (Glasgow Warriors).
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.