He was born in Copenhagen to physician Einar Böcher and wife Cathinca née Andersen. Steen B. Böcher, professor of geography, was his brother.
Tyge Böcher was professor of botany at the University of Copenhagen from 1954 to 1979. He was a prolific scientific writer, leaving some 250 scholarly books and articles. His scientific research covered as diverse phylogenetic lineages as vascular plants, bryophytes, lichens and algae and a broad set of disciplines from anatomy, ecology and evolution of plant species to the ecology of plant populations and plant communities. He was particularly interested in chromosomal and ecological races of plant species. He did field work in Greenland, Denmark, various European mountain regions and in Argentina. His investigation of the Greenland flora were particularly ground-breaking.
He was a co-founder of Flora Europaea and he authored the Flora of Greenland (1968).
Studies on the vegetation of the East coast of Greenland between Scoresby Sound and Angmagsalik (Christian IX's Land). Meddelelser om Grønland 104, 4. 1933
Botany. Appendix to Ejnar Mikkelsen: The Blosseville Coast of East Greenland. Geographical Journal (London) 81: 400-402. 1933. [1]
Keywords: Greenland, arctic vegetation
Om en måde til undersøgelse af konstans, skudtæthed og homogenitet (Eng. summ. On a method for investigating constancy, shoots density and homogeneity). Botanisk Tidsskrift 43: 278-304. 1935.
Udbredelsen af Ericaceæ, Vacciniaceæ og Empetraceæ i Danmark. Summary: The distribution of the Ericaceæ, Vacciniaceæ and Empetraceæ in Denmark (Danmarks topografisk-botaniske Undersøgelse Nr. 3). Botanisk Tidsskrift 44: 5-40, 12 maps. 1937.
Nogle studier over Færøernes alpine vegetation [Zusammenfassung: Einige Studien über die alpine Vegetation der Färöer Inseln]. Botanisk Tidsskrift 44: 154-201. 1937.
Vegetationen på Randbøl Hede. Med særlig hensyntagen til det fredede areal. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 1, 3: 1-234. 1941.
Beiträge zur Pflanzengeographie und Ökologie dänischer Vegetation. 1. Über die Flechtenheiden und Dünen der Insel Läsö. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 2, 1: 1-38. 1941.
Studies on the plant geography of the North-Atlantic heath formation II. Danish dwarf shrub communities in relation to those of Northern Europe. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 2, 7: 1-130. 1943.
Beiträge zur Pflanzengeographie und Ökologie Dänischer Vegetation. II. Über die Waldsaum- und Graskrautgesellschaften trockener und halbtrockener Böden der Insel Seeland mit besonderer Berücksichtigung der Strandabhänge und Strandebenen. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 4, 1: 1-163. 1945.
Meiosis in Anemone apennina with special reference to chiasma localisation. Hereditas 31: 221-237. 1945.
Keywords: cytology
Ochromonas viridis sp.n., a green flagellate belonging to Chrysomonadinae. Videnskabelige meddelelser fra Dansk Naturhistorisk Forening 108: 233-238. 1945.
& T. Christensen & M.S. Christiansen. Slope and dune vegetation of North Jutland. I. Himmerland. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 4, 4: 1-78. 1946.
Studies on the sapropelic flora of the lake Flyndersø with special reference to the Oscillatoriaceae. Biologiske Meddelelser / Kongelige Danske Videnskabernes Selskab 21, 1: 1-46. 1949.
A. Noe-Nygaard, Chr. Vibe T.W. Böcher & E. Holtved. Notes on Danish scientific work since 1939. Arctic 4: 50-56. 1951. [3]
Botanical investigations in South West Greenland, 1946. Arctic 4 (1): 46-49. 1951. [4]
Studies on morphological progression and evolution in the vegetable kingdom. Biologiske Meddelelser / Kongelige Danske Videnskabernes Selskab 18, 13: 1-51. 1951.
& K. Holmen & K. Jakobsen. Grønlands flora (ill. by Ingeborg Frederiksen). København. 313 pp. 1957. (2nd edn 1966; Engl. edn. ‘’’Flora of Greenland’’’ 1968; 3rd edn 1978).
& K. Larsen. Geographical distribution of initiation of flowering, growth habit, and other characters in Holcus lanatus L. Botaniska Notiser 111: 289-300. 1958.
The evolution of Arctic and montane plant taxa in the light of chromosome studies and comparative cultivations. Proc. 9. Internat. Bot. Congr. II A: 3-4. 1959.
Floristic and taxonomic activity in Denmark since 1945 essential to the work of Flora Europaea. Floristic Reports, Flora Europaea Genova Symposium 21–28 May 1961: 1-8, 1961.
The development of cytotaxonomy since Darwin's time. In: A Darwin Centenary”, P.J. Wanstall (ed.): 26-43. 1961.
The evolution of Arctic and montane plant taxa in the light of chromosome studies and comparative cultivations. In: Recent Advances in Botany (Toronto): 925-928. 1961.
The study of ecotypical variation in relation to experimental morphology. (Symposium on biosystematics, Montreal 1962). Regnum Vegetabile 27: 10-16. 1963.
Experimental and cytological studies on plant species. IX. Some Arctic and montane Crucifers. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 14, 7: 1-74. 1966.
Experimental and cytological studies on plant species. X. Sisyrinchium with special reference to the Greenland representative. Botanisk Tidsskrift 61: 273-290. 1966.
Experimental and cytological studies on plant species. XI. North Atlantic tetraploids of the Campanula rotundifolia complex. Annales Botanici Fennici 3: 287-298. 1966.
& O.B. Lyshede. Anatomical studies on xerophytic apophyllous plants. II. Additional species from South American shrub steppes. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 18, 4: 1-137. 1972.
Phytogeography of Greenland (Survey and methods). In: B.A. Yurtsev, The Arctic floristic region, papers read at the symposium "Floristic delimitation and subdivision of the Arctic", 8 July, 1975 in Leningrad; 127-142. 1978.