Currently, there is not enough scientific evidence to confirm if having antibodies means you are definitely immune.
At the time of writing, some human reinfections with SARS-CoV-2 have been confirmed in patients who had antibodies but this is extremely rare. This suggests the body usually develops significant immunity as antibody levels seem to rise in patients as viral counts drop and reinfections are very uncommon.
We also do not know how long any immunity to Covid-19 lasts. Currently, research suggests antibody levels can slowly fall in people who had asymptomatic exposure. Whether this means they are more prone to reinfection is unknown.
Following the 2002 SARS virus outbreak, the responsible virus SARS-CoV was studied extensively. Research showed patients with antibodies were immune over a 3 year period. Covid-19 (SARS-Cov2) is closely related to SARS-CoV, both viruses having originated in bats. Please see this article for further information.