Solari was born in Rosario, Santa Fe. After unsuccessfully emerging through Club Atlético Vélez Sarsfield's youth ranks, he made his professional debuts with Estudiantes de La Plata. He also represented in his country, without much impact overall, Defensa y Justicia, Argentinos Juniors and Gimnasia y Esgrima de Jujuy.
After one year in Italy with amateurs A.C. Chioggia Sottomarina, Solari joined K. Lierse S.K. in the Belgian Pro League in the 2004 summer, scoring five goals in his only season to help his team finish in tenth position. Subsequently he signed for APOEL FC in Cyprus, extending his contract until 2008 after impressing in his first year – 14 league goals in only 16 starts, Cypriot Cup conquest.
In 2006–07, Solari finished top scorer in the First Division (20 goals) as the Nicosia-based club won its third national championship in six years. He was also voted the league's MVP but, at the end of May 2007, agreed on a transfer to UNAM Pumas of Mexico, once again winning an individual scoring accolade after netting 15 times in the Apertura alone.
On 15 June 2008 Solari was transferred to Spanish side UD Almería, who paid €3.8 million to UNAM. He made his La Liga debut on 31 August playing 14 minutes in a 3–1 away win against Athletic Bilbao, but finished his first season with only eight games, scoring his only official goal for the Andalusians in a 1–2 loss at CD Numancia.
On 2 June 2010, 30-year-old Solari signed for three years with former club APOEL. He immediately made an impact by scoring four goals in six appearances in the season's UEFA Europa League, going on to add 11 in 28 in the domestic league, which again ended in conquest.
Solari was regularly used in the team's 2011–12 UEFA Champions League campaign, having in total seven appearances. On 4 April 2012, he scored from a penalty kick in a 2–5 quarter-final loss against Real Madrid at the Santiago Bernabéu (2–8 on aggregate).
Solari was hit by several injuries in 2012–13 and, as a result, appeared in only three matches all competitions comprised. On 5 January 2013 his contract with APOEL was terminated by mutual consent, and late into the same month he signed with fellow league side Apollon Limassol.
On 16 July 2013, Solari moved teams and countries again, penning a deal with Superleague Greece club Skoda Xanthi FC. Roughly one year later, he signed for Dalian Aerbin F.C. from the Chinese Super League.
Solari returned to Greece and its top flight on 6 February 2015, signing a six-month contract with Ergotelis FC. He subsequently competed in the Ecuadorian Serie A, with C.D. Cuenca and S.D. Aucas.
Solari is nicknamed "Tano", which means "Italian" in Argentinian slang. His father Eduardo, and two of his four siblings, older Santiago and younger David, were also footballers, with the former playing with individual and team success for Real Madrid and Inter Milan.
His uncle Jorge played for several clubs during his career, mostly Club Atlético River Plate, whilst cousin Fernando Redondo also represented Real Madrid. All but David won caps for Argentina.APOEL
Cypriot First Division: 2006–07, 2010–11
Cypriot Cup: 2005–06
Cypriot Super Cup: 2011
Cypriot Cup: 2012–13
Cypriot First Division: Top scorer & MVP 2006–07
Mexican Primera División: Top scorer 2007–08 (Apertura and Clausura)
Superleague Greece: Top scorer 2013–14