Another option is using the SuperTab plugin:
" if you use Vundle, load plugins:
Bundle 'ervandew/supertab'
Bundle 'Valloric/YouCompleteMe'
Bundle 'SirVer/ultisnips'
" make YCM compatible with UltiSnips (using supertab)
let g:ycm_key_list_select_completion = ['<C-n>', '<Down>']
let g:ycm_key_list_previous_completion = ['<C-p>', '<Up>']
let g:SuperTabDefaultCompletionType="<C-n>"
" better key bindings for UltiSnipsExpandTrigger
let g:UltiSnipsExpandTrigger = "<tab>"
let g:UltiSnipsJumpForwardTrigger = "<tab>"
let g:UltiSnipsJumpBackwardTrigger = "<s-tab>"
Here YouCompleteMe is bound to a different combination Ctrln, but then that combination is bound to tab through SuperTab. UltiSnips and SuperTab play nice together, so you can then just bind UltiSnips to tab directly and everything will work out.