Reja replaced Vladimir Petkovic, who was officially sacked on Saturday following persistent speculation about his Lazio future.
Petkovic agreed during the Christmas break to take charge of Switzerland after this summer's World Cup, reportedly breaching his club contract in doing so.
Reja, who led Lazio to a fourth-placed finish before deciding to leave the club in the summer of 2012, inherits a team which sits in 10th place in Serie A and have won just one of their last eight league games.
"We need to understand that we are a strong team," Reja said to La Repubblica newspaper.
"We deserve to be in a better position in the standings."
Lazio, who are competing in the Europa League this year, have not won on the road this season and go into Monday's encounter at the Stadio Olimpico on the back of a 4-1 loss at Hellas Verona.
Moreover, the Biancoceleste have lost two of their last three league games at home.
Despite Lazio's troubles, opponents Inter will not take them lightly.
"It's always difficult to play against Lazio," Inter midfielder Jonathan said. "We will face a strong team that has very good players.
"They will be motivated by the change of coach and they will all want to prove their worth.
"We expect a difficult game but so can they.
"We want to do well, especially after the winning the derby and we want to take home three points."
Inter, coached by Walter Mazzarri, ended 2013 in the best possible way by beating city rivals AC Milan 1-0 to halt a four-match winless run.
The result, courtesy of Rodrigo Palacio's late goal, lifted Inter to fifth place, five points adrift of Napoli, who are third and hold the last Champions League qualifying spot.
"We need to find continuity," Jonathan said. "We should have won a lot more games than we have so far but due to lack of concentration at certain stages of a match, we have thrown away points along the way.
"This is something we need to improve on and point higher."
The Nerazzurri will be without Argentinian defender Hugo Campagnaro, who serves a one-match ban.
Moreover, defender Christian Chivu and midfielder Saphir Taider are both out injured.
Rodrigo Palacio, who has scored 10 goals in 17 league appearances for Inter this season, will lead the Nerazzurri's attack.