The 32-year-old arrives as a free agent after his contract with Diego Simeone's Atletico Madrid ended last June.
Lemar and Herrera join Mario Hermoso, Joao Felix and Moussa Dembele on a list of five Atletico players currently out after contracting the illness. Atletico have been hit hard by the virus, with eight players previously having tested positive besides coach Diego Simeone.
Dembele will join Atletico until the end of the season when the club will have the option to buy him permanently for around 35 million euros.
The 24-year-old Dembele has scored 45 goals in 105 games for French leader Lyon, but has lost his place in the side to Tino Kadewere this season. His Lyon contract runs until June 2023 but sporting director Juninho will not stand in his way.
Costa arrived at Atletico in 2006 at the age of 17, going on to play 215 matches over two spells (2010-14 and then 2018-20) either side of three seasons at Chelsea, scoring 83 goals and providing 36 assists.
Costa will miss Atletico's Champions League game at home to Lokomotiv Moscow on Wednesday and is expected to be out for at least a month.
Champions League: Thigh injury rules out Atletico Madrid striker Diego Costa for Bayern Munich clash
Atletico did not specify for how long the 32-year-old would be absent due to the knock, which forced him off the field during his side's 2-0 win at Celta Vigo on Saturday.
LaLiga: Luis Suarez, Diego Costa 'can play together for sure,' says Atletico Madrid manager Diego Simeone
The 33-year-old forward Suarez joined Atletico after six seasons at Barcelona with Costa, 31, saying he welcomed the arrival but would fight for his place in the side.
LaLiga: Lionel Messi scores in first game since Barcelona transfer dispute; Luis Suarez nets brace for Atletico Madrid
Luis Suarez, whose departure was confirmed on Thursday, marked his Atletico Madrid debut by scoring twice in a 6-1 win over Granada.
Atletico Madrid's Diego Costa and Santiago Arias test positive for COVID-19, both players asymptomatic
Before the resumption of training on Friday, the entire Atletico Madrid first team squad underwent tests except for Costa and Arias.
LaLiga: Barcelona keep title race alive with narrow win over Valladolid; Atletico Madrid edge past Real Betis
Other than his assist for Vidal, Messi was limited to a pair of shots, including a free kick that Masip palmed over his bar.
LaLiga: Lionel Messi records 700th goal in Barcelona's bitter draw to Atletico Madrid; Real Mallorca thump Celta Vigo
Barcelona’s third draw in four rounds left it in second place, one point behind leader Real Madrid.
LaLiga: Iago Aspas' late strike helps Celta Vigo hold Barcelona to thrilling 2-2 draw; Atletico Madrid beat Alaves
Quique Setien’s Barcelona twice threw away their lead against Celta Vigo and despite climbing to the top of the table with 69 points, can be pushed back to second if Real Madrid win against Espanyol on Sunday.
Spanish prosecutors indict former Real Madrid coach Carlo Ancelotti on suspicion of avoiding $1.12 million in taxes
As well as working for Real Madrid and Everton, Ancelotti has had trophy-laden spells at other European clubs including AC Milan, Chelsea, Paris St Germain and Bayern Munich.
LaLiga: Marcelo takes knee as Real Madrid make winning return to league; Atletico held to draw at Athletic Bilbao
Real Madrid resumed their Spanish league campaign with a 3-1 win over Eibar on Sunday to keep pace with leader Barcelona.
Atletico Madrid forward Diego Costa arrives in Madrid court to ratify pact reached in tax fraud case
Atletico Madrid forward Diego Costa appeared in court wearing a white mask in the Spanish capital on Thursday to ratify a pact he made with prosecutors to resolve a tax fraud case against him.
Atletico Madrid forward Diego Costa is to face trial on 4 June for tax fraud in 2014, a court filing showed on Friday, with prosecutors asking the Spain international to be handed a six-month jail sentence and a fine of €507,208 ($564,877).
Champions League: Once leaders in player conditioning, Atletico Madrid wrestle with injury crisis as Liverpool visit
Compared to an all-powerful Liverpool side on course for a record-smashing Premier League title triumph, Atletico Madrid certainly look vulnerable
LaLiga: Atletico Madrid striker Alvaro Morata sidelined with muscle injury as club's forward crisis deepens
Morata suffered the injury during the 1-0 derby defeat by Real Madrid on Saturday which left his side sixth and 13 points behind their rivals who are top of La Liga.
Atletico stayed in sixth place with 26 points from 16 matches, five points behind leaders Barcelona and Real Madrid, which both have two games in hand on Atletico entering the weekend — including one against each other on 18 December.