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."
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.
