The former Spain coach has been appointed until the end of the season, after Onesimo Sanchez was sacked after only two months at the helm on Monday, with the side lying 19th in the 20-team league.
Some members of the squad have been accused by fans of lacking commitment and professionalism in recent weeks.
"I am a coach who gets involved in the dressing room, who likes to talk to players, very demanding but a believer in team spirit," Clemente told reporters.
"I come down very hard on anyone who doesn't show complete commitment. This is a joint commitment to represent a team and a city in a delicate situation."
Clemente has a huge job on his hands. His predecessor managed to win only six points in the 30 available after he replaced Jose Luis Mendilibar at the beginning of February.
The 60-year-old, Valladolid's third coach of the campaign, has eight matches left to avoid relegation starting at 18th-placed Tenerife on Saturday. The team are seven points from safety.
Clemente coached Spain between 1992 and 1998, and has also worked with Serbia and a number of clubs including Athletic Bilbao, Atletico Madrid, Espanyol, Olympique Marseille, Real Betis and Real Sociedad.
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