Tickets are already on sale for the Europe-wide event, which boosted the country's reputation this year when Estonians Tanel Pudar and Dave Benton came out on top. It takes place on May 25.
Matvere told The Baltic Times he was surprised by the proposal.
"Although I was not going to take part in the contest to host the event, the organizers decided to choose me, and I am grateful for their trust."
He added that hosting such a public event would be a personal first. "I have received hundreds of proposals, but Eurovision is on another scale for me - a mega-, giga- or whatever times greater event," said the 33-year-old actor.
Matvere said his colleagues were already making fun of him and predicting future successes on stage and screen. "But that's nonsense. I don't think my career will somehow skyrocket as a result," said Matvere, who has worked at Tallinn City Theater since 1992. "We are just employed as talking heads."
Mezzo-soprano Peebo, 30, has worked with the Vienna Opera since 1997 and also starred in a French musical called "Les Lecons Tenebres." She told ETV her latest appointment had already caught the attention of the Austrian media with some magazines planning cover stories about her.
"The Vienna Opera is proud of me," she beamed.
Peebo and Matvere were chosen from nine candidates, all of them ready to demonstrate their command of English and French, their attractive appearance, sense of humor, intelligence and stage experience.
Estonian composers and poets have submitted a record 90 songs to the organizing committee. Only 10 will pass to the final round, and only one, of course, will represent Estonia at the contest of 24 countries.
ETV offered 1,500 tickets for the final concert of the contest on Dec. 12 at an online auction with a starting price of 4,500 kroons ($260), which is slightly less than the average monthly salary in Estonia.
The rest of the 6,000 seats are reserved for the contestants and their teams.
More seats will be available for two preliminary concerts on the mornings of May 24 and May 25 with tickets costing from 150 kroons to 490 kroons available from Jan. 28.
Peeter Rebane, the producer of the contest, said the more money that could be made from ticket sales, the less the burden would be on the national budget.
Aare Kilp, a prominent Estonian businessman and ex-chairman of Hoiubank, bought 10 VIP seats in the hall for 1,875 kroons, and is now trying to make a profit by selling the overpriced tickets.
Kilp told the SL Ohtuleht daily he hoped to earn as much as 500,000 kroons from the Eurovision contest.