Alexei Vasiliev graduated from the St Petersburg State Rimsky-Korsakov Conservatoire in 1995 as a cellist (class of Anatoly Nikitin). While still a student he began to work in the cello section of the Academic Symphony Orchestra of the St Petersburg Philharmonic, Honoured Ensemble of Russia, in addition to teaching. Currently teaches cello at the St Petersburg State Conservatoire, the Middle Special School of Music of the Conservatoire and the St Petersburg Rimsky-Korsakov School of Music.
Actively appears in concert as a soloist and together with instrumental ensembles. Has performed with the Symphony Orchestra of the St Petersburg Philharmonic, Honoured Ensemble of Russia, the Symphony Orchestra of the St Petersburg Academic Capella, the St Petersburg Symphony Orchestra and the St Petersburg State Academic Symphony Orchestra. Has collaborated with the conductors Leo Korchin, Ravil Martynov, Algirdas Paulavičius, Vladimir Begletsov and Alexander Chernushenko.
Since 2006 he has directed the St Petersburg Rimsky-Korsakov School of Music. Since 2008 he has led an orchestral class at the St Petersburg Rimsky-Korsakov School of Music, and heads the Algirdas Paulavičius Youth Symphony Orchestra. The ensemble has made a name for itself at the finest concert venues in St Petersburg and tours to towns and cities throughout Russia and Europe. Liana Isakadze, Pavel Yegorov, Sergei Slovachevsky, Alexei Massarsky, Martti Rousi, Daniil Trifonov and Pavel Milyukov are among numerous other artists to have appeared with the ensemble.
In August 2015 Vasiliev became Acting Rector of the St Petersburg State Conservatoire. In December 2016 he was elected its Rector.