Correspondence to be sent to: alja123@gmail.com Thomassen conjectured that there is a function f (k) such that every strongly f (k)-connected tournament contains k edge-disjoint Hamiltonian cycles. This conjecture was recently proved by Kühn, Lapinskas, Osthus, and Patel who showed that f (k) ≤ O(k 2 (log k) 2 ) and conjectured that there is a constant C such that f (k) ≤ Ck 2 . We prove this conjecture. As a second application of our methods we answer a question of Thomassen about spanning linkages in highly connected tournaments.