This Letter presents the first study of Higgs boson production in association with a vector boson (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>V</a:mi><a:mo>=</a:mo><a:mi>W</a:mi></a:math> or <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>Z</c:mi></c:math>) in the fully hadronic <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>q</e:mi><e:mi>q</e:mi><e:mi>b</e:mi><e:mi>b</e:mi></e:math> final state using data recorded by the ATLAS detector at the LHC in proton-proton collisions at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msqrt><g:mrow><g:mi>s</g:mi></g:mrow></g:msqrt><g:mo>=</g:mo><g:mn>13</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>TeV</g:mi></g:mrow></g:math> and corresponding to an integrated luminosity of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mn>137</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:msup><i:mrow><i:mi>fb</i:mi></i:mrow><i:mrow><i:mo>−</i:mo><i:mn>1</i:mn></i:mrow></i:msup></i:mrow></i:math>. The vector bosons and Higgs bosons are each reconstructed as large-radius jets and tagged using jet substructure techniques. Dedicated tagging algorithms exploiting <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>b</k:mi></k:math>-tagging properties are used to identify jets consistent with Higgs bosons decaying into <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>b</m:mi><m:mover accent="true"><m:mi>b</m:mi><m:mo stretchy="false">¯</m:mo></m:mover></m:math>. Dominant backgrounds from multijet production are determined directly from the data, and a likelihood fit to the jet mass distribution of Higgs boson candidates is used to extract the number of signal events. The <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>V</q:mi><q:mi>H</q:mi></q:math> production cross section is measured inclusively and differentially in several ranges of Higgs boson transverse momentum: 250–450, 450–650, and greater than 650 GeV. The inclusive signal yield relative to the standard model expectation is observed to be <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi>μ</s:mi><s:mo>=</s:mo><s:msubsup><s:mrow><s:mn>1.4</s:mn></s:mrow><s:mrow><s:mo>−</s:mo><s:mn>0.9</s:mn></s:mrow><s:mrow><s:mo>+</s:mo><s:mn>1.0</s:mn></s:mrow></s:msubsup></s:mrow></s:math> and the corresponding cross section is <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mn>3.1</u:mn><u:mo>±</u:mo><u:mn>1.3</u:mn><u:mo stretchy="false">(</u:mo><u:mrow><u:mi>stat</u:mi></u:mrow><u:msubsup><u:mrow><u:mo stretchy="false">)</u:mo></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>1.4</u:mn></u:mrow><u:mrow><u:mo>+</u:mo><u:mn>1.8</u:mn></u:mrow></u:msubsup><u:mo stretchy="false">(</u:mo><u:mrow><u:mi>syst</u:mi></u:mrow><u:mo stretchy="false">)</u:mo><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>pb</u:mi></u:mrow></u:math>. © 2024 CERN, for the ATLAS Collaboration 2024 CERN