Mr Beattie, MSP for Midlothian North and Musselburgh, was in charge of the party's finances from 2004 to last year when Mr Chapman was voted in by members in November.
However, Mr Chapman stepped down two weeks ago, citing a lack of “financial information”.
Mr Beattie and Dunfermline and West Fife MP Mr Chapman were the only candidates for the post at the vote last year. If other candidates had run, the party would have recalculated the votes, but the lack of competition left Mr Beattie as the only candidate who could be appointed.
Questions have been raised over the whereabouts of a £600,000 fund donated to the SNP by members to help pay for a new referendum.
The party had said the funds, raised through SNP websites since 2017, would be ring-fenced for a future independence referendum campaign. However, its most recent accounts showed the SNP had just £96,000 in the bank at the end of 2019.
Police Scotland is currently looking into a complaint of alleged financial irregularity and will decide whether to carry out a full investigation.
Previously announcing his resignation, Mr Chapman said on Twitter: “Despite having a resounding mandate from members to introduce more transparency into the party’s finances, I have not received the support or financial information to carry out the fiduciary duties of National Treasurer. Regretfully I have resigned with immediate effect.”
The SNP has been contacted for comment.