Objectives: Many meta-research studies have investigated rates and predictors of data and code sharing in medicine. However, most of these studies have been narrow in scope and modest in size. We aimed to synthesise the findings of this body of research to provide an accurate picture of how common data and code sharing is, how this frequency has changed over time, and what factors are associated with sharing. Design: Systematic review with meta-analysis of individual participant data (IPD) from meta-research studies. Data sources: Ovid MEDLINE, Ovid Embase, MetaArXiv, medRxiv, and bioRxiv were searched from inception to July 1st, 2021. Eligibility criteria: Studies that investigated data or code sharing across a sample of scientific articles presenting original medical and health research. Data extraction and synthesis: Two authors independently screened records, assessed risk of bias, and extracted summary data from study reports. IPD were requested from authors when not publicly available. Key outcomes of interest were the prevalence of statements that declared data or code were publicly available, or "available on request" (declared availability), and the success rates of retrieving these products (actual availability). The associations between data and code availability and several factors (e.g., journal policy, data type, study design, research subjects) were also examined. A two-stage approach to IPD meta-analysis was performed, with proportions and risk ratios pooled using the Hartung-Knapp-Sidik-Jonkman method for random-effects meta-analysis. Three-level random-effects meta-regressions were also performed to evaluate the influence of publication year on sharing rate. Results: 105 meta-research studies examining 2,121,580 articles across 31 specialties were included in the review. Eligible studies examined a median of 195 primary articles (IQR: 113-475), with a median publication year of 2015 (IQR: 2012-2018). Only eight studies (8%) were classified as low risk of bias. Useable IPD were assembled for 100 studies (2,121,197 articles), of which 94 datasets passed independent reproducibility checks. Meta-analyses revealed declared and actual public data availability rates of 8% (95% CI: 5-11%, 95% PI: 0-30%, k=27, o=700,054) and 2% (95% CI: 1-3%, 95% PI: 0-11%, k=25, o=11,873) respectively since 2016. Meta-regression indicated that only declared data sharing rates have increased significantly over time. For public code sharing, both declared and actual availability rates were estimated to be less than 0.5% since 2016, and neither demonstrated any meaningful increases over time. Only 33% of authors (95% CI: 5-69%, k=3, o=429) were estimated to comply with mandatory data sharing policies of journals. Conclusion: Code sharing remains persistently low across medicine and health research. In contrast, declarations of data sharing are also low, but they are increasing. However, they do not always correspond to the actual sharing of data. Mandatory data sharing policies of journals may also not be as effective as expected, and may vary in effectiveness according to data type - a finding that may be informative for policymakers when designing policies and allocating resources to audit compliance.