His company, America Movil, has controlled Austria's largest telecommunications company since July.
The second largest shareholder remains Austria's state holding company ÖIAG, which retains its 28.4 percent stake.
Slim offered other shareholders €7.15 per share, and extended the deadline for the offer up to Thursday of last week.
The largest telecommunications company in Latin America, America Movil plans to use Telekom Austria as a base to grow into Eastern Europe.
Telekom Austria plans this year to make a capital increase in order to finance the expansion, among other activities.
The Austrian company sustained significant losses in the first half of this year.